<?xml version="1.0" encoding="UTF-8"?>

<!--XBRL Document Created with the Workiva Platform-->
<!--Copyright 2026 Workiva-->
<!--r:019eb1ae-c3d3-767b-94f8-78830ad1444d,g:e00f2797-3d0d-4dfb-82f7-5723821decd2-->
<link:linkbase xmlns:link="http://www.xbrl.org/2003/linkbase" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://www.xbrl.org/2003/linkbase http://www.xbrl.org/2003/xbrl-linkbase-2003-12-31.xsd">
  <link:roleRef roleURI="http://www.xbrl.org/2009/role/negatedPeriodStartLabel" xlink:type="simple" xlink:href="http://www.xbrl.org/lrr/role/negated-2009-12-16.xsd#negatedPeriodStartLabel"/>
  <link:roleRef roleURI="http://www.xbrl.org/2009/role/netLabel" xlink:type="simple" xlink:href="http://www.xbrl.org/lrr/role/net-2009-12-16.xsd#netLabel"/>
  <link:roleRef roleURI="http://www.xbrl.org/2009/role/negatedNetLabel" xlink:type="simple" xlink:href="http://www.xbrl.org/lrr/role/negated-2009-12-16.xsd#negatedNetLabel"/>
  <link:roleRef roleURI="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="simple" xlink:href="http://www.xbrl.org/lrr/role/negated-2009-12-16.xsd#negatedTerseLabel"/>
  <link:roleRef roleURI="http://www.xbrl.org/2009/role/negatedPeriodEndLabel" xlink:type="simple" xlink:href="http://www.xbrl.org/lrr/role/negated-2009-12-16.xsd#negatedPeriodEndLabel"/>
  <link:roleRef roleURI="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="simple" xlink:href="http://www.xbrl.org/lrr/role/negated-2009-12-16.xsd#negatedLabel"/>
  <link:roleRef roleURI="http://www.xbrl.org/2009/role/negatedTotalLabel" xlink:type="simple" xlink:href="http://www.xbrl.org/lrr/role/negated-2009-12-16.xsd#negatedTotalLabel"/>
  <link:labelLink xlink:role="http://www.xbrl.org/2003/role/link" xlink:type="extended">
    <link:label id="lab_fbc_EBPEmployerContributionNonvestedAmount_019eb1ae-c48c-7090-a19a-25a22ff7f2c8_terseLabel_en-US" xlink:label="lab_fbc_EBPEmployerContributionNonvestedAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Nonvested amount</link:label>
    <link:label id="lab_fbc_EBPEmployerContributionNonvestedAmount_label_en-US" xlink:label="lab_fbc_EBPEmployerContributionNonvestedAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Employer Contribution, Nonvested Amount</link:label>
    <link:label id="lab_fbc_EBPEmployerContributionNonvestedAmount_documentation_en-US" xlink:label="lab_fbc_EBPEmployerContributionNonvestedAmount" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">EBP, Employer Contribution, Nonvested Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_EBPEmployerContributionNonvestedAmount" xlink:href="fbc-20260610.xsd#fbc_EBPEmployerContributionNonvestedAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_EBPEmployerContributionNonvestedAmount" xlink:to="lab_fbc_EBPEmployerContributionNonvestedAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseForParticipantContributionRollover_019eb1ae-c48c-7655-8bc3-c7954362b16c_terseLabel_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseForParticipantContributionRollover" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Rollover contributions</link:label>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseForParticipantContributionRollover_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseForParticipantContributionRollover" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Change in Net Asset Available for Benefit, Increase from Participant Contribution, Rollover</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseForParticipantContributionRollover" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseForParticipantContributionRollover"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseForParticipantContributionRollover" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseForParticipantContributionRollover" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_MaximumMember_019eb1ae-c48c-7a99-bd7b-172e84baf78f_terseLabel_en-US" xlink:label="lab_srt_MaximumMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Maximum</link:label>
    <link:label id="lab_srt_MaximumMember_label_en-US" xlink:label="lab_srt_MaximumMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Maximum [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MaximumMember" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_MaximumMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_MaximumMember" xlink:to="lab_srt_MaximumMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_LegalEntityAxis_019eb1ae-c48c-78ce-92d2-ee6ebd8005b0_terseLabel_en-US" xlink:label="lab_dei_LegalEntityAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Legal Entity [Axis]</link:label>
    <link:label id="lab_dei_LegalEntityAxis_label_en-US" xlink:label="lab_dei_LegalEntityAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Legal Entity [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_LegalEntityAxis" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_LegalEntityAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_LegalEntityAxis" xlink:to="lab_dei_LegalEntityAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_RangeMember_019eb1ae-c48c-7e1c-abf5-d4e74300f7c8_terseLabel_en-US" xlink:label="lab_srt_RangeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statistical Measurement [Domain]</link:label>
    <link:label id="lab_srt_RangeMember_label_en-US" xlink:label="lab_srt_RangeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statistical Measurement [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RangeMember" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_RangeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_RangeMember" xlink:to="lab_srt_RangeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanDescriptionOfPlanTable_019eb1ae-c48c-7b72-8755-700027f1f10e_terseLabel_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanDescriptionOfPlanTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">EBP, Description of Plan [Table]</link:label>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanDescriptionOfPlanTable_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanDescriptionOfPlanTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Description of Plan [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanDescriptionOfPlanTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanDescriptionOfPlanTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanDescriptionOfPlanTable" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanDescriptionOfPlanTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MutualFundMember_019eb1ae-c48c-70dd-8352-762b9af4c079_terseLabel_en-US" xlink:label="lab_us-gaap_MutualFundMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Mutual Funds</link:label>
    <link:label id="lab_us-gaap_MutualFundMember_label_en-US" xlink:label="lab_us-gaap_MutualFundMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Mutual Fund [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MutualFundMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MutualFundMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MutualFundMember" xlink:to="lab_us-gaap_MutualFundMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanScheduleOfDelinquentParticipantContributionCorrected_019eb1ae-c48c-7052-9a88-3cc889850f0f_terseLabel_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanScheduleOfDelinquentParticipantContributionCorrected" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total fully corrected under VFCP and PTE 2002-51</link:label>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanScheduleOfDelinquentParticipantContributionCorrected_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanScheduleOfDelinquentParticipantContributionCorrected" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Schedule of Delinquent Participant Contribution, Corrected</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanScheduleOfDelinquentParticipantContributionCorrected" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanScheduleOfDelinquentParticipantContributionCorrected"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanScheduleOfDelinquentParticipantContributionCorrected" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanScheduleOfDelinquentParticipantContributionCorrected" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanRelatedPartyAndPartyInInterestTransactionsTable_019eb1ae-c48c-7976-8e94-695c52591d40_terseLabel_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanRelatedPartyAndPartyInInterestTransactionsTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">EBP, Related Party and Party-in-Interest Transactions [Table]</link:label>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanRelatedPartyAndPartyInInterestTransactionsTable_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanRelatedPartyAndPartyInInterestTransactionsTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Related Party and Party-in-Interest Transactions [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanRelatedPartyAndPartyInInterestTransactionsTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanRelatedPartyAndPartyInInterestTransactionsTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanRelatedPartyAndPartyInInterestTransactionsTable" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanRelatedPartyAndPartyInInterestTransactionsTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanFullyBenefitResponsiveInvestmentContractTable_019eb1ae-c48c-7cf7-b467-bb68455b476a_terseLabel_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanFullyBenefitResponsiveInvestmentContractTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">EBP, Fully Benefit-Responsive Investment Contract [Table]</link:label>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanFullyBenefitResponsiveInvestmentContractTable_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanFullyBenefitResponsiveInvestmentContractTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Fully Benefit-Responsive Investment Contract [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanFullyBenefitResponsiveInvestmentContractTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanFullyBenefitResponsiveInvestmentContractTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanFullyBenefitResponsiveInvestmentContractTable" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanFullyBenefitResponsiveInvestmentContractTable" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_EBPParticipantContributionContributionToEligibleCompensationPercentage_019eb1ae-c48c-76de-a37b-0e8a652084c8_terseLabel_en-US" xlink:label="lab_fbc_EBPParticipantContributionContributionToEligibleCompensationPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Annual fixed rate contribution, percentage</link:label>
    <link:label id="lab_fbc_EBPParticipantContributionContributionToEligibleCompensationPercentage_label_en-US" xlink:label="lab_fbc_EBPParticipantContributionContributionToEligibleCompensationPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Participant Contribution, Contribution to Eligible Compensation, Percentage</link:label>
    <link:label id="lab_fbc_EBPParticipantContributionContributionToEligibleCompensationPercentage_documentation_en-US" xlink:label="lab_fbc_EBPParticipantContributionContributionToEligibleCompensationPercentage" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">EBP, Participant Contribution, Contribution to Eligible Compensation, Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_EBPParticipantContributionContributionToEligibleCompensationPercentage" xlink:href="fbc-20260610.xsd#fbc_EBPParticipantContributionContributionToEligibleCompensationPercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_EBPParticipantContributionContributionToEligibleCompensationPercentage" xlink:to="lab_fbc_EBPParticipantContributionContributionToEligibleCompensationPercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitDecrease_019eb1ae-c48c-7341-ad87-2c34d9857ade_totalLabel_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitDecrease" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total deductions</link:label>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitDecrease_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitDecrease" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Change in Net Asset Available for Benefit, Decrease</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitDecrease" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitDecrease"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitDecrease" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitDecrease" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_EBPSafeHarborMatchingContributionTrancheOneMember_019eb1ae-c48c-79bc-807f-cc04b81fa06e_terseLabel_en-US" xlink:label="lab_fbc_EBPSafeHarborMatchingContributionTrancheOneMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">EBP, Safe Harbor Matching Contribution, Tranche One</link:label>
    <link:label id="lab_fbc_EBPSafeHarborMatchingContributionTrancheOneMember_label_en-US" xlink:label="lab_fbc_EBPSafeHarborMatchingContributionTrancheOneMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Safe Harbor Matching Contribution, Tranche One [Member]</link:label>
    <link:label id="lab_fbc_EBPSafeHarborMatchingContributionTrancheOneMember_documentation_en-US" xlink:label="lab_fbc_EBPSafeHarborMatchingContributionTrancheOneMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">EBP, Safe Harbor Matching Contribution, Tranche One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_EBPSafeHarborMatchingContributionTrancheOneMember" xlink:href="fbc-20260610.xsd#fbc_EBPSafeHarborMatchingContributionTrancheOneMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_EBPSafeHarborMatchingContributionTrancheOneMember" xlink:to="lab_fbc_EBPSafeHarborMatchingContributionTrancheOneMember" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_EBPNoteReceivableFromParticipantAccountPrimaryResidenceMaximumBorrowingTerm_019eb1ae-c48c-7e58-bb63-6f5a22d4ac04_terseLabel_en-US" xlink:label="lab_fbc_EBPNoteReceivableFromParticipantAccountPrimaryResidenceMaximumBorrowingTerm" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Primary residence, borrowing term</link:label>
    <link:label id="lab_fbc_EBPNoteReceivableFromParticipantAccountPrimaryResidenceMaximumBorrowingTerm_label_en-US" xlink:label="lab_fbc_EBPNoteReceivableFromParticipantAccountPrimaryResidenceMaximumBorrowingTerm" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Note Receivable From Participant, Account, Primary Residence, Maximum Borrowing Term</link:label>
    <link:label id="lab_fbc_EBPNoteReceivableFromParticipantAccountPrimaryResidenceMaximumBorrowingTerm_documentation_en-US" xlink:label="lab_fbc_EBPNoteReceivableFromParticipantAccountPrimaryResidenceMaximumBorrowingTerm" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">EBP, Note Receivable From Participant, Account, Primary Residence, Maximum Borrowing Term</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_EBPNoteReceivableFromParticipantAccountPrimaryResidenceMaximumBorrowingTerm" xlink:href="fbc-20260610.xsd#fbc_EBPNoteReceivableFromParticipantAccountPrimaryResidenceMaximumBorrowingTerm"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_EBPNoteReceivableFromParticipantAccountPrimaryResidenceMaximumBorrowingTerm" xlink:to="lab_fbc_EBPNoteReceivableFromParticipantAccountPrimaryResidenceMaximumBorrowingTerm" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanNoteReceivableFromParticipantAccountMaximumBorrowingAmount_019eb1ae-c48c-7f11-9491-e0e3da17f9e7_terseLabel_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanNoteReceivableFromParticipantAccountMaximumBorrowingAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Note receivable from participant, account, maximum borrowing, amount</link:label>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanNoteReceivableFromParticipantAccountMaximumBorrowingAmount_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanNoteReceivableFromParticipantAccountMaximumBorrowingAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Note Receivable from Participant, Account, Maximum Borrowing, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanNoteReceivableFromParticipantAccountMaximumBorrowingAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanNoteReceivableFromParticipantAccountMaximumBorrowingAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanNoteReceivableFromParticipantAccountMaximumBorrowingAmount" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanNoteReceivableFromParticipantAccountMaximumBorrowingAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanInvestmentFairValueAndNavTextBlock_019eb1ae-c48c-75ff-89c7-c3687fd82416_terseLabel_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanInvestmentFairValueAndNavTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investments</link:label>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanInvestmentFairValueAndNavTextBlock_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanInvestmentFairValueAndNavTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Investment, Fair Value and NAV [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanInvestmentFairValueAndNavTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanInvestmentFairValueAndNavTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanInvestmentFairValueAndNavTextBlock" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanInvestmentFairValueAndNavTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanFullyBenefitResponsiveInvestmentContractAbstract_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanFullyBenefitResponsiveInvestmentContractAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Fully Benefit-Responsive Investment Contract [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanFullyBenefitResponsiveInvestmentContractAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanFullyBenefitResponsiveInvestmentContractAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanFullyBenefitResponsiveInvestmentContractAbstract" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanFullyBenefitResponsiveInvestmentContractAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_EBPEmployerContributionTypeDomain_019eb1ae-c48c-7a72-9f0c-73e3d75f95fe_terseLabel_en-US" xlink:label="lab_fbc_EBPEmployerContributionTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">EBP, Employer Contribution, Type [Domain]</link:label>
    <link:label id="lab_fbc_EBPEmployerContributionTypeDomain_label_en-US" xlink:label="lab_fbc_EBPEmployerContributionTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Employer Contribution, Type [Domain]</link:label>
    <link:label id="lab_fbc_EBPEmployerContributionTypeDomain_documentation_en-US" xlink:label="lab_fbc_EBPEmployerContributionTypeDomain" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">EBP, Employer Contribution, Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_EBPEmployerContributionTypeDomain" xlink:href="fbc-20260610.xsd#fbc_EBPEmployerContributionTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_EBPEmployerContributionTypeDomain" xlink:to="lab_fbc_EBPEmployerContributionTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanInvestmentExcludingPlanInterestInMasterTrustFairValue_019eb1ae-c48c-7eee-82ca-f5b138512a06_terseLabel_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanInvestmentExcludingPlanInterestInMasterTrustFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total investments</link:label>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanInvestmentExcludingPlanInterestInMasterTrustFairValue_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanInvestmentExcludingPlanInterestInMasterTrustFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Investment, Excluding Plan Interest in Master Trust, Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanInvestmentExcludingPlanInterestInMasterTrustFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanInvestmentExcludingPlanInterestInMasterTrustFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanInvestmentExcludingPlanInterestInMasterTrustFairValue" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanInvestmentExcludingPlanInterestInMasterTrustFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MoneyMarketFundsMember_019eb1ae-c48c-7460-aae2-09cf5a0131f5_terseLabel_en-US" xlink:label="lab_us-gaap_MoneyMarketFundsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Money Market Fund</link:label>
    <link:label id="lab_us-gaap_MoneyMarketFundsMember_label_en-US" xlink:label="lab_us-gaap_MoneyMarketFundsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Money Market Funds [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MoneyMarketFundsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MoneyMarketFundsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MoneyMarketFundsMember" xlink:to="lab_us-gaap_MoneyMarketFundsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueInputsLevel1Member_019eb1ae-c48c-7358-9f79-b1e75ef0a6e8_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel1Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Quoted Prices in Active Markets for Identical Assets (Level 1)</link:label>
    <link:label id="lab_us-gaap_FairValueInputsLevel1Member_label_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel1Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Inputs, Level 1 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueInputsLevel1Member" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueInputsLevel1Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueInputsLevel1Member" xlink:to="lab_us-gaap_FairValueInputsLevel1Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanAsset_019eb1ae-c48c-72fd-883a-25c6432d74e6_totalLabel_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanAsset" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total assets</link:label>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanAsset_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanAsset" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Asset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanAsset" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanAsset"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanAsset" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanAsset" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanAssetAbstract_019eb1ae-c48c-7304-9222-6464bdbfd80a_terseLabel_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanAssetAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Assets:</link:label>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanAssetAbstract_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanAssetAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Asset [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanAssetAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanAssetAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanAssetAbstract" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanAssetAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_RangeAxis_019eb1ae-c48c-76f2-84fc-b2ae11aee274_terseLabel_en-US" xlink:label="lab_srt_RangeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statistical Measurement [Axis]</link:label>
    <link:label id="lab_srt_RangeAxis_label_en-US" xlink:label="lab_srt_RangeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statistical Measurement [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RangeAxis" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_RangeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_RangeAxis" xlink:to="lab_srt_RangeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseAbstract_019eb1ae-c48c-7ad3-bf92-0b9a4774affc_terseLabel_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Additions to net assets attributed to:</link:label>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseAbstract_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Change in Net Asset Available for Benefit, Increase [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseAbstract" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanStatementOfChangeInNetAssetAvailableForBenefitTable_019eb1ae-c48c-77aa-a486-7f14b34f4aff_terseLabel_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanStatementOfChangeInNetAssetAvailableForBenefitTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">EBP, Statement of Change in Net Asset Available for Benefit [Table]</link:label>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanStatementOfChangeInNetAssetAvailableForBenefitTable_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanStatementOfChangeInNetAssetAvailableForBenefitTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Statement of Change in Net Asset Available for Benefit [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanStatementOfChangeInNetAssetAvailableForBenefitTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanStatementOfChangeInNetAssetAvailableForBenefitTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanStatementOfChangeInNetAssetAvailableForBenefitTable" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanStatementOfChangeInNetAssetAvailableForBenefitTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanPaymentToParticipantPolicyTextBlock_019eb1ae-c48c-70aa-9fa8-07ecfa2cbee9_terseLabel_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanPaymentToParticipantPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Payment of Benefits</link:label>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanPaymentToParticipantPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanPaymentToParticipantPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Payment to Participant [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanPaymentToParticipantPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanPaymentToParticipantPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanPaymentToParticipantPolicyTextBlock" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanPaymentToParticipantPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_AmendmentFlag_019eb1ae-c48c-7ad3-bdc9-c2c42b531b46_terseLabel_en-US" xlink:label="lab_dei_AmendmentFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amendment Flag</link:label>
    <link:label id="lab_dei_AmendmentFlag_label_en-US" xlink:label="lab_dei_AmendmentFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Amendment Flag</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_AmendmentFlag" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_AmendmentFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_AmendmentFlag" xlink:to="lab_dei_AmendmentFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanBasisOfAccountingPolicyTextBlock_019eb1ae-c48c-7984-8332-9b06f2cd0d95_terseLabel_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanBasisOfAccountingPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Basis of Presentation</link:label>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanBasisOfAccountingPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanBasisOfAccountingPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Basis of Accounting [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanBasisOfAccountingPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanBasisOfAccountingPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanBasisOfAccountingPolicyTextBlock" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanBasisOfAccountingPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanScheduleOfAssetHeldForInvestmentTable_019eb1ae-c48c-7835-96f5-67f6c96b4bd9_terseLabel_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanScheduleOfAssetHeldForInvestmentTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">EBP, Schedule of Asset Held for Investment [Table]</link:label>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanScheduleOfAssetHeldForInvestmentTable_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanScheduleOfAssetHeldForInvestmentTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Schedule of Asset Held for Investment [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanScheduleOfAssetHeldForInvestmentTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanScheduleOfAssetHeldForInvestmentTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanScheduleOfAssetHeldForInvestmentTable" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanScheduleOfAssetHeldForInvestmentTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanReceivableInvestmentSale_019eb1ae-c48c-70ed-b73d-88f28dd4c527_terseLabel_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanReceivableInvestmentSale" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due from broker</link:label>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanReceivableInvestmentSale_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanReceivableInvestmentSale" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Investment Sale, Receivable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanReceivableInvestmentSale" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanReceivableInvestmentSale"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanReceivableInvestmentSale" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanReceivableInvestmentSale" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanInvestmentNumberOfShares_019eb1ae-c48c-7e4e-8642-effc30f38b19_terseLabel_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanInvestmentNumberOfShares" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of shares/units</link:label>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanInvestmentNumberOfShares_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanInvestmentNumberOfShares" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Investment, Number of Shares</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanInvestmentNumberOfShares" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanInvestmentNumberOfShares"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanInvestmentNumberOfShares" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanInvestmentNumberOfShares" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanDescriptionOfPlanAbstract_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanDescriptionOfPlanAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Description of Plan and Accounting Change [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanDescriptionOfPlanAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanDescriptionOfPlanAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanDescriptionOfPlanAbstract" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanDescriptionOfPlanAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanReceivableAbstract_019eb1ae-c48c-73fb-857b-3bd497a983b1_terseLabel_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanReceivableAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Receivables:</link:label>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanReceivableAbstract_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanReceivableAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Receivable [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanReceivableAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanReceivableAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanReceivableAbstract" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanReceivableAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanInvestmentFairValueAndNavTableTextBlock_019eb1ae-c48c-74a1-8ba3-5e48e49bb0e1_terseLabel_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanInvestmentFairValueAndNavTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment, Fair Value and NAV</link:label>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanInvestmentFairValueAndNavTableTextBlock_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanInvestmentFairValueAndNavTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Investment, Fair Value and NAV [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanInvestmentFairValueAndNavTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanInvestmentFairValueAndNavTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanInvestmentFairValueAndNavTableTextBlock" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanInvestmentFairValueAndNavTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_EBPNonExemptTransactionsAbstract_label_en-US" xlink:label="lab_fbc_EBPNonExemptTransactionsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Non-exempt Transactions [Abstract]</link:label>
    <link:label id="lab_fbc_EBPNonExemptTransactionsAbstract_documentation_en-US" xlink:label="lab_fbc_EBPNonExemptTransactionsAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">EBP, Non-exempt Transactions</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_EBPNonExemptTransactionsAbstract" xlink:href="fbc-20260610.xsd#fbc_EBPNonExemptTransactionsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_EBPNonExemptTransactionsAbstract" xlink:to="lab_fbc_EBPNonExemptTransactionsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_EBPOneYearButLessThanTwoMember_019eb1ae-c48c-7121-beb4-5b2a5b5d294e_terseLabel_en-US" xlink:label="lab_fbc_EBPOneYearButLessThanTwoMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">1 year but less than 2</link:label>
    <link:label id="lab_fbc_EBPOneYearButLessThanTwoMember_label_en-US" xlink:label="lab_fbc_EBPOneYearButLessThanTwoMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, One Year But Less Than Two [Member]</link:label>
    <link:label id="lab_fbc_EBPOneYearButLessThanTwoMember_documentation_en-US" xlink:label="lab_fbc_EBPOneYearButLessThanTwoMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">EBP, One Year But Less Than Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_EBPOneYearButLessThanTwoMember" xlink:href="fbc-20260610.xsd#fbc_EBPOneYearButLessThanTwoMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_EBPOneYearButLessThanTwoMember" xlink:to="lab_fbc_EBPOneYearButLessThanTwoMember" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_EBPChangeInNetAssetAvailableForBenefitIncreaseDecreaseFromOtherIncome_019eb1ae-c48c-7634-9441-532fdb6ce541_terseLabel_en-US" xlink:label="lab_fbc_EBPChangeInNetAssetAvailableForBenefitIncreaseDecreaseFromOtherIncome" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other income</link:label>
    <link:label id="lab_fbc_EBPChangeInNetAssetAvailableForBenefitIncreaseDecreaseFromOtherIncome_label_en-US" xlink:label="lab_fbc_EBPChangeInNetAssetAvailableForBenefitIncreaseDecreaseFromOtherIncome" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Change in Net Asset Available for Benefit, Increase (Decrease) From Other Income</link:label>
    <link:label id="lab_fbc_EBPChangeInNetAssetAvailableForBenefitIncreaseDecreaseFromOtherIncome_documentation_en-US" xlink:label="lab_fbc_EBPChangeInNetAssetAvailableForBenefitIncreaseDecreaseFromOtherIncome" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">EBP, Change in Net Asset Available for Benefit, Increase (Decrease) From Other Income</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_EBPChangeInNetAssetAvailableForBenefitIncreaseDecreaseFromOtherIncome" xlink:href="fbc-20260610.xsd#fbc_EBPChangeInNetAssetAvailableForBenefitIncreaseDecreaseFromOtherIncome"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_EBPChangeInNetAssetAvailableForBenefitIncreaseDecreaseFromOtherIncome" xlink:to="lab_fbc_EBPChangeInNetAssetAvailableForBenefitIncreaseDecreaseFromOtherIncome" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanScheduleOfDelinquentParticipantContributionAbstract_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanScheduleOfDelinquentParticipantContributionAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Schedule of Delinquent Participant Contribution [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanScheduleOfDelinquentParticipantContributionAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanScheduleOfDelinquentParticipantContributionAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanScheduleOfDelinquentParticipantContributionAbstract" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanScheduleOfDelinquentParticipantContributionAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentTypeCategorizationMember_019eb1ae-c48c-791c-a569-b3f83a47e59c_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentTypeCategorizationMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investments [Domain]</link:label>
    <link:label id="lab_us-gaap_InvestmentTypeCategorizationMember_label_en-US" xlink:label="lab_us-gaap_InvestmentTypeCategorizationMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investments [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentTypeCategorizationMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentTypeCategorizationMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentTypeCategorizationMember" xlink:to="lab_us-gaap_InvestmentTypeCategorizationMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanUseOfEstimatePolicyTextBlock_019eb1ae-c48c-72c4-a2e0-118175de2653_terseLabel_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanUseOfEstimatePolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Use of Estimates</link:label>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanUseOfEstimatePolicyTextBlock_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanUseOfEstimatePolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Use of Estimate [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanUseOfEstimatePolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanUseOfEstimatePolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanUseOfEstimatePolicyTextBlock" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanUseOfEstimatePolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanScheduleOfAssetHeldForInvestmentTableTextBlock_019eb1ae-c48c-74db-88dc-0035178f0ce3_terseLabel_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanScheduleOfAssetHeldForInvestmentTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">EBP, Schedule of Asset Held for Investment</link:label>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanScheduleOfAssetHeldForInvestmentTableTextBlock_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanScheduleOfAssetHeldForInvestmentTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Schedule of Asset Held for Investment [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanScheduleOfAssetHeldForInvestmentTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanScheduleOfAssetHeldForInvestmentTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanScheduleOfAssetHeldForInvestmentTableTextBlock" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanScheduleOfAssetHeldForInvestmentTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_CoverAbstract_label_en-US" xlink:label="lab_dei_CoverAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cover [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CoverAbstract" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_CoverAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_CoverAbstract" xlink:to="lab_dei_CoverAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_EBPEmployerContributionDiscretionaryEmployerContribution_019eb1ae-c48c-7df6-b6cd-1d7fe0400a8a_terseLabel_en-US" xlink:label="lab_fbc_EBPEmployerContributionDiscretionaryEmployerContribution" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Employer contribution vesting amount</link:label>
    <link:label id="lab_fbc_EBPEmployerContributionDiscretionaryEmployerContribution_label_en-US" xlink:label="lab_fbc_EBPEmployerContributionDiscretionaryEmployerContribution" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Employer Contribution, Discretionary Employer Contribution</link:label>
    <link:label id="lab_fbc_EBPEmployerContributionDiscretionaryEmployerContribution_documentation_en-US" xlink:label="lab_fbc_EBPEmployerContributionDiscretionaryEmployerContribution" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">EBP, Employer Contribution, Discretionary Employer Contribution</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_EBPEmployerContributionDiscretionaryEmployerContribution" xlink:href="fbc-20260610.xsd#fbc_EBPEmployerContributionDiscretionaryEmployerContribution"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_EBPEmployerContributionDiscretionaryEmployerContribution" xlink:to="lab_fbc_EBPEmployerContributionDiscretionaryEmployerContribution" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanRiskAndUncertaintyTextBlock_019eb1ae-c48c-765b-9786-0574f778cfbb_terseLabel_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanRiskAndUncertaintyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Risks and Uncertainties</link:label>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanRiskAndUncertaintyTextBlock_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanRiskAndUncertaintyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Risk and Uncertainty [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanRiskAndUncertaintyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanRiskAndUncertaintyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanRiskAndUncertaintyTextBlock" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanRiskAndUncertaintyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseForEmployerContributionCash_019eb1ae-c48c-7c4f-92db-47978061ed74_terseLabel_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseForEmployerContributionCash" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Participant contributions</link:label>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseForEmployerContributionCash_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseForEmployerContributionCash" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Change in Net Asset Available for Benefit, Increase from Employer Contribution, Cash</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseForEmployerContributionCash" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseForEmployerContributionCash"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseForEmployerContributionCash" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseForEmployerContributionCash" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanScheduleOfDelinquentParticipantContributionLineItems_019eb1ae-c48c-724c-bd4f-e4795e9626f2_terseLabel_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanScheduleOfDelinquentParticipantContributionLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">EBP, Schedule of Delinquent Participant Contribution [Line Items]</link:label>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanScheduleOfDelinquentParticipantContributionLineItems_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanScheduleOfDelinquentParticipantContributionLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Schedule of Delinquent Participant Contribution [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanScheduleOfDelinquentParticipantContributionLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanScheduleOfDelinquentParticipantContributionLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanScheduleOfDelinquentParticipantContributionLineItems" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanScheduleOfDelinquentParticipantContributionLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_MinimumMember_019eb1ae-c48c-7e4a-b298-6b0e4f0c379b_terseLabel_en-US" xlink:label="lab_srt_MinimumMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Minimum</link:label>
    <link:label id="lab_srt_MinimumMember_label_en-US" xlink:label="lab_srt_MinimumMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Minimum [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MinimumMember" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_MinimumMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_MinimumMember" xlink:to="lab_srt_MinimumMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseForInterestIncomeOnNoteReceivableFromParticipant_019eb1ae-c48c-79d1-883f-084ef4f775d9_terseLabel_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseForInterestIncomeOnNoteReceivableFromParticipant" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest on notes receivable from participants</link:label>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseForInterestIncomeOnNoteReceivableFromParticipant_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseForInterestIncomeOnNoteReceivableFromParticipant" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Change in Net Asset Available for Benefit, Increase from Interest Income on Note Receivable from Participant</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseForInterestIncomeOnNoteReceivableFromParticipant" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseForInterestIncomeOnNoteReceivableFromParticipant"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseForInterestIncomeOnNoteReceivableFromParticipant" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseForInterestIncomeOnNoteReceivableFromParticipant" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentTypeAxis_019eb1ae-c48c-7860-aaf1-cb4b70a927b2_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment Type [Axis]</link:label>
    <link:label id="lab_us-gaap_InvestmentTypeAxis_label_en-US" xlink:label="lab_us-gaap_InvestmentTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentTypeAxis" xlink:to="lab_us-gaap_InvestmentTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseForContribution_019eb1ae-c48c-723d-b0f4-f80ba2149f7c_totalLabel_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseForContribution" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total contributions</link:label>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseForContribution_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseForContribution" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Change in Net Asset Available for Benefit, Increase from Contribution</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseForContribution" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseForContribution"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseForContribution" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseForContribution" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseForParticipantContributionExcludingRollover_019eb1ae-c48c-7fe1-b21d-f23ae9c7daa9_terseLabel_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseForParticipantContributionExcludingRollover" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Employer contributions</link:label>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseForParticipantContributionExcludingRollover_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseForParticipantContributionExcludingRollover" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Change in Net Asset Available for Benefit, Increase from Participant Contribution, Excluding Rollover</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseForParticipantContributionExcludingRollover" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseForParticipantContributionExcludingRollover"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseForParticipantContributionExcludingRollover" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseForParticipantContributionExcludingRollover" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseDecreaseForGainLossOnInvestment_019eb1ae-c48c-73ec-a246-e9e9941ad073_terseLabel_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseDecreaseForGainLossOnInvestment" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net appreciation in fair value of investments</link:label>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseDecreaseForGainLossOnInvestment_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseDecreaseForGainLossOnInvestment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Change in Net Asset Available for Benefit, Increase (Decrease) from Gain (Loss) on Investment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseDecreaseForGainLossOnInvestment" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseDecreaseForGainLossOnInvestment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseDecreaseForGainLossOnInvestment" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseDecreaseForGainLossOnInvestment" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanDescriptionOfPlanLineItems_019eb1ae-c48c-7a68-8784-80495657d718_terseLabel_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanDescriptionOfPlanLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">EBP, Description of Plan [Line Items]</link:label>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanDescriptionOfPlanLineItems_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanDescriptionOfPlanLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Description of Plan [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanDescriptionOfPlanLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanDescriptionOfPlanLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanDescriptionOfPlanLineItems" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanDescriptionOfPlanLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanDescriptionOfPlanTextBlock_019eb1ae-c48c-71d7-8afe-2dab3cadb0a0_terseLabel_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanDescriptionOfPlanTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Description of the Plan</link:label>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanDescriptionOfPlanTextBlock_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanDescriptionOfPlanTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Description of Plan [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanDescriptionOfPlanTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanDescriptionOfPlanTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanDescriptionOfPlanTextBlock" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanDescriptionOfPlanTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanScheduleOfDelinquentParticipantContributionPendingCorrectionInVfcp_019eb1ae-c48c-7570-bee0-8405b61ceb23_terseLabel_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanScheduleOfDelinquentParticipantContributionPendingCorrectionInVfcp" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Contributions pending correction in VFCP</link:label>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanScheduleOfDelinquentParticipantContributionPendingCorrectionInVfcp_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanScheduleOfDelinquentParticipantContributionPendingCorrectionInVfcp" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Schedule of Delinquent Participant Contribution, Pending Correction in VFCP</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanScheduleOfDelinquentParticipantContributionPendingCorrectionInVfcp" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanScheduleOfDelinquentParticipantContributionPendingCorrectionInVfcp"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanScheduleOfDelinquentParticipantContributionPendingCorrectionInVfcp" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanScheduleOfDelinquentParticipantContributionPendingCorrectionInVfcp" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanStatementOfChangeInNetAssetAvailableForBenefitLineItems_019eb1ae-c48c-7e92-a6ad-2403db382e9f_terseLabel_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanStatementOfChangeInNetAssetAvailableForBenefitLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">EBP, Statement of Change in Net Asset Available for Benefit [Line Items]</link:label>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanStatementOfChangeInNetAssetAvailableForBenefitLineItems_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanStatementOfChangeInNetAssetAvailableForBenefitLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Statement of Change in Net Asset Available for Benefit [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanStatementOfChangeInNetAssetAvailableForBenefitLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanStatementOfChangeInNetAssetAvailableForBenefitLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanStatementOfChangeInNetAssetAvailableForBenefitLineItems" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanStatementOfChangeInNetAssetAvailableForBenefitLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanStatementOfNetAssetAvailableForBenefitTable_019eb1ae-c48c-757d-af27-f91bc02c7836_terseLabel_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanStatementOfNetAssetAvailableForBenefitTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">EBP, Statement of Net Asset Available for Benefit [Table]</link:label>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanStatementOfNetAssetAvailableForBenefitTable_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanStatementOfNetAssetAvailableForBenefitTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Statement of Net Asset Available for Benefit [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanStatementOfNetAssetAvailableForBenefitTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanStatementOfNetAssetAvailableForBenefitTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanStatementOfNetAssetAvailableForBenefitTable" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanStatementOfNetAssetAvailableForBenefitTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanScheduleOfAssetHeldForInvestmentLineItems_019eb1ae-c48c-7666-9395-642a7fca85e4_terseLabel_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanScheduleOfAssetHeldForInvestmentLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">EBP, Schedule of Asset Held for Investment [Line Items]</link:label>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanScheduleOfAssetHeldForInvestmentLineItems_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanScheduleOfAssetHeldForInvestmentLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Schedule of Asset Held for Investment [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanScheduleOfAssetHeldForInvestmentLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanScheduleOfAssetHeldForInvestmentLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanScheduleOfAssetHeldForInvestmentLineItems" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanScheduleOfAssetHeldForInvestmentLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanContributionPolicyTextBlock_019eb1ae-c48c-7be1-b150-60c59976c0ec_terseLabel_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanContributionPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Contributions</link:label>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanContributionPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanContributionPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Contribution [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanContributionPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanContributionPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanContributionPolicyTextBlock" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanContributionPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanScheduleOfAssetHeldForInvestmentAbstract_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanScheduleOfAssetHeldForInvestmentAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Schedule of Asset Held for Investment [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanScheduleOfAssetHeldForInvestmentAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanScheduleOfAssetHeldForInvestmentAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanScheduleOfAssetHeldForInvestmentAbstract" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanScheduleOfAssetHeldForInvestmentAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanAccountingPolicyTable_019eb1ae-c48c-7b98-ba5c-b6cf2f950648_terseLabel_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanAccountingPolicyTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">EBP, Accounting Policy [Table]</link:label>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanAccountingPolicyTable_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanAccountingPolicyTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Accounting Policy [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanAccountingPolicyTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanAccountingPolicyTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanAccountingPolicyTable" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanAccountingPolicyTable" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_EBPDividendsPaidToParticipants_019eb1ae-c48c-79fa-ba37-64d9ccc5bdce_terseLabel_en-US" xlink:label="lab_fbc_EBPDividendsPaidToParticipants" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Dividends paid to participants</link:label>
    <link:label id="lab_fbc_EBPDividendsPaidToParticipants_label_en-US" xlink:label="lab_fbc_EBPDividendsPaidToParticipants" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Dividends Paid To Participants</link:label>
    <link:label id="lab_fbc_EBPDividendsPaidToParticipants_documentation_en-US" xlink:label="lab_fbc_EBPDividendsPaidToParticipants" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">EBP, Dividends Paid To Participants</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_EBPDividendsPaidToParticipants" xlink:href="fbc-20260610.xsd#fbc_EBPDividendsPaidToParticipants"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_EBPDividendsPaidToParticipants" xlink:to="lab_fbc_EBPDividendsPaidToParticipants" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncrease_019eb1ae-c48c-75b9-89b5-efb041063497_totalLabel_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncrease" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total additions</link:label>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncrease_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncrease" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Change in Net Asset Available for Benefit, Increase</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncrease" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncrease"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncrease" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncrease" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_EBPRequisiteServicePeriodAxis_019eb1ae-c48c-77be-90f3-2e3e31b6a8d3_terseLabel_en-US" xlink:label="lab_fbc_EBPRequisiteServicePeriodAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">EBP, Requisite Service Period [Axis]</link:label>
    <link:label id="lab_fbc_EBPRequisiteServicePeriodAxis_label_en-US" xlink:label="lab_fbc_EBPRequisiteServicePeriodAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Requisite Service Period [Axis]</link:label>
    <link:label id="lab_fbc_EBPRequisiteServicePeriodAxis_documentation_en-US" xlink:label="lab_fbc_EBPRequisiteServicePeriodAxis" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">EBP, Requisite Service Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_EBPRequisiteServicePeriodAxis" xlink:href="fbc-20260610.xsd#fbc_EBPRequisiteServicePeriodAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_EBPRequisiteServicePeriodAxis" xlink:to="lab_fbc_EBPRequisiteServicePeriodAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_EBPParticipantAccountsAdministrativeFee_019eb1ae-c48c-7990-96c2-2cec2df87698_terseLabel_en-US" xlink:label="lab_fbc_EBPParticipantAccountsAdministrativeFee" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Administrative fee</link:label>
    <link:label id="lab_fbc_EBPParticipantAccountsAdministrativeFee_label_en-US" xlink:label="lab_fbc_EBPParticipantAccountsAdministrativeFee" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Participant Accounts, Administrative Fee</link:label>
    <link:label id="lab_fbc_EBPParticipantAccountsAdministrativeFee_documentation_en-US" xlink:label="lab_fbc_EBPParticipantAccountsAdministrativeFee" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">EBP, Participant Accounts, Administrative Fee</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_EBPParticipantAccountsAdministrativeFee" xlink:href="fbc-20260610.xsd#fbc_EBPParticipantAccountsAdministrativeFee"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_EBPParticipantAccountsAdministrativeFee" xlink:to="lab_fbc_EBPParticipantAccountsAdministrativeFee" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_EBPPlanTerminationAbstract_label_en-US" xlink:label="lab_fbc_EBPPlanTerminationAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Plan Termination [Abstract]</link:label>
    <link:label id="lab_fbc_EBPPlanTerminationAbstract_documentation_en-US" xlink:label="lab_fbc_EBPPlanTerminationAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">EBP, Plan Termination</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_EBPPlanTerminationAbstract" xlink:href="fbc-20260610.xsd#fbc_EBPPlanTerminationAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_EBPPlanTerminationAbstract" xlink:to="lab_fbc_EBPPlanTerminationAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseDecreaseForIncomeLossOnInvestmentAbstract_019eb1ae-c48c-7b44-b23f-460785bd40e1_terseLabel_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseDecreaseForIncomeLossOnInvestmentAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment income:</link:label>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseDecreaseForIncomeLossOnInvestmentAbstract_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseDecreaseForIncomeLossOnInvestmentAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Change in Net Asset Available for Benefit, Increase (Decrease) from Income (Loss) on Investment [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseDecreaseForIncomeLossOnInvestmentAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseDecreaseForIncomeLossOnInvestmentAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseDecreaseForIncomeLossOnInvestmentAbstract" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseDecreaseForIncomeLossOnInvestmentAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentIdentifierAxis_019eb1ae-c48c-78d7-8742-46a3bcdfbf66_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentIdentifierAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment, Identifier [Axis]</link:label>
    <link:label id="lab_us-gaap_InvestmentIdentifierAxis_label_en-US" xlink:label="lab_us-gaap_InvestmentIdentifierAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment, Identifier [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentIdentifierAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentIdentifierAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentIdentifierAxis" xlink:to="lab_us-gaap_InvestmentIdentifierAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_EBPThreeOrMoreYearsMember_019eb1ae-c48c-75b6-96b3-2a04a40b7dd9_terseLabel_en-US" xlink:label="lab_fbc_EBPThreeOrMoreYearsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">3 or more years</link:label>
    <link:label id="lab_fbc_EBPThreeOrMoreYearsMember_label_en-US" xlink:label="lab_fbc_EBPThreeOrMoreYearsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Three Or More Years [Member]</link:label>
    <link:label id="lab_fbc_EBPThreeOrMoreYearsMember_documentation_en-US" xlink:label="lab_fbc_EBPThreeOrMoreYearsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">EBP, Three Or More Years</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_EBPThreeOrMoreYearsMember" xlink:href="fbc-20260610.xsd#fbc_EBPThreeOrMoreYearsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_EBPThreeOrMoreYearsMember" xlink:to="lab_fbc_EBPThreeOrMoreYearsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_EBPEmployerContributionVestingPercentage_019eb1ae-c48c-7a0f-a63e-87e71bea0ce9_terseLabel_en-US" xlink:label="lab_fbc_EBPEmployerContributionVestingPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">EBP, Employer contribution vesting percentage</link:label>
    <link:label id="lab_fbc_EBPEmployerContributionVestingPercentage_label_en-US" xlink:label="lab_fbc_EBPEmployerContributionVestingPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Employer Contribution Vesting Percentage</link:label>
    <link:label id="lab_fbc_EBPEmployerContributionVestingPercentage_documentation_en-US" xlink:label="lab_fbc_EBPEmployerContributionVestingPercentage" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">EBP, Employer Contribution Vesting Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_EBPEmployerContributionVestingPercentage" xlink:href="fbc-20260610.xsd#fbc_EBPEmployerContributionVestingPercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_EBPEmployerContributionVestingPercentage" xlink:to="lab_fbc_EBPEmployerContributionVestingPercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitDecreaseForAdministrativeExpense_019eb1ae-c48c-7074-b830-846973ee9ca7_terseLabel_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitDecreaseForAdministrativeExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Administrative expenses</link:label>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitDecreaseForAdministrativeExpense_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitDecreaseForAdministrativeExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Change in Net Asset Available for Benefit, Decrease from Administrative Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitDecreaseForAdministrativeExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitDecreaseForAdministrativeExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitDecreaseForAdministrativeExpense" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitDecreaseForAdministrativeExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanAssetHeldForInvestment_019eb1ae-c48c-71b9-b059-e5bd0218f445_verboseLabel_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanAssetHeldForInvestment" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Asset held</link:label>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanAssetHeldForInvestment_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanAssetHeldForInvestment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Asset Held for Investment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanAssetHeldForInvestment" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanAssetHeldForInvestment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanAssetHeldForInvestment" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanAssetHeldForInvestment" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentInformationLineItems_019eb1ae-c48c-7969-a615-c5978eb0c3b6_terseLabel_en-US" xlink:label="lab_dei_DocumentInformationLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Information [Line Items]</link:label>
    <link:label id="lab_dei_DocumentInformationLineItems_label_en-US" xlink:label="lab_dei_DocumentInformationLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Information [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentInformationLineItems" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentInformationLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentInformationLineItems" xlink:to="lab_dei_DocumentInformationLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_EBPEmployerContributionTypeAxis_019eb1ae-c48c-7dc0-8ad3-fba5dd3fbce2_terseLabel_en-US" xlink:label="lab_fbc_EBPEmployerContributionTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">EBP, Employer Contribution, Type [Axis]</link:label>
    <link:label id="lab_fbc_EBPEmployerContributionTypeAxis_label_en-US" xlink:label="lab_fbc_EBPEmployerContributionTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Employer Contribution, Type [Axis]</link:label>
    <link:label id="lab_fbc_EBPEmployerContributionTypeAxis_documentation_en-US" xlink:label="lab_fbc_EBPEmployerContributionTypeAxis" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">EBP, Employer Contribution, Type</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_EBPEmployerContributionTypeAxis" xlink:href="fbc-20260610.xsd#fbc_EBPEmployerContributionTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_EBPEmployerContributionTypeAxis" xlink:to="lab_fbc_EBPEmployerContributionTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EbpRiskAndUncertaintyLineItems_019eb1ae-c48c-7b31-8312-0a452c0826bc_terseLabel_en-US" xlink:label="lab_us-gaap-ebp_EbpRiskAndUncertaintyLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">EBP, Risk and Uncertainty [Line Items]</link:label>
    <link:label id="lab_us-gaap-ebp_EbpRiskAndUncertaintyLineItems_label_en-US" xlink:label="lab_us-gaap-ebp_EbpRiskAndUncertaintyLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Risk and Uncertainty [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EbpRiskAndUncertaintyLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EbpRiskAndUncertaintyLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EbpRiskAndUncertaintyLineItems" xlink:to="lab_us-gaap-ebp_EbpRiskAndUncertaintyLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EbpRiskAndUncertaintyTable_019eb1ae-c48c-7b19-981f-ec515a33d851_terseLabel_en-US" xlink:label="lab_us-gaap-ebp_EbpRiskAndUncertaintyTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">EBP, Risk and Uncertainty [Table]</link:label>
    <link:label id="lab_us-gaap-ebp_EbpRiskAndUncertaintyTable_label_en-US" xlink:label="lab_us-gaap-ebp_EbpRiskAndUncertaintyTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Risk and Uncertainty [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EbpRiskAndUncertaintyTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EbpRiskAndUncertaintyTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EbpRiskAndUncertaintyTable" xlink:to="lab_us-gaap-ebp_EbpRiskAndUncertaintyTable" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_EBPTwoYearsButLessThanThreeMember_019eb1ae-c48c-7bcd-9fdb-5b116bb8c82b_terseLabel_en-US" xlink:label="lab_fbc_EBPTwoYearsButLessThanThreeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2 years but less than 3</link:label>
    <link:label id="lab_fbc_EBPTwoYearsButLessThanThreeMember_label_en-US" xlink:label="lab_fbc_EBPTwoYearsButLessThanThreeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Two Years But Less Than Three [Member]</link:label>
    <link:label id="lab_fbc_EBPTwoYearsButLessThanThreeMember_documentation_en-US" xlink:label="lab_fbc_EBPTwoYearsButLessThanThreeMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">EBP, Two Years But Less Than Three</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_EBPTwoYearsButLessThanThreeMember" xlink:href="fbc-20260610.xsd#fbc_EBPTwoYearsButLessThanThreeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_EBPTwoYearsButLessThanThreeMember" xlink:to="lab_fbc_EBPTwoYearsButLessThanThreeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_EBPScheduleOfVestingPercentagesTableTextBlock_019eb1ae-c48c-7aaf-9cd7-55ccff65f9b1_terseLabel_en-US" xlink:label="lab_fbc_EBPScheduleOfVestingPercentagesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">EBP, Schedule of Vesting Percentages</link:label>
    <link:label id="lab_fbc_EBPScheduleOfVestingPercentagesTableTextBlock_label_en-US" xlink:label="lab_fbc_EBPScheduleOfVestingPercentagesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Schedule Of Vesting Percentages [Table Text Block]</link:label>
    <link:label id="lab_fbc_EBPScheduleOfVestingPercentagesTableTextBlock_documentation_en-US" xlink:label="lab_fbc_EBPScheduleOfVestingPercentagesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">EBP, Schedule Of Vesting Percentages</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_EBPScheduleOfVestingPercentagesTableTextBlock" xlink:href="fbc-20260610.xsd#fbc_EBPScheduleOfVestingPercentagesTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_EBPScheduleOfVestingPercentagesTableTextBlock" xlink:to="lab_fbc_EBPScheduleOfVestingPercentagesTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanEmployerContributionParticipantCompensationMatchedPercentage_019eb1ae-c48c-7749-92e1-ff6443d88579_terseLabel_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanEmployerContributionParticipantCompensationMatchedPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Participant compensation matched, percentage</link:label>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanEmployerContributionParticipantCompensationMatchedPercentage_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanEmployerContributionParticipantCompensationMatchedPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Employer Contribution, Participant Compensation Matched, Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanEmployerContributionParticipantCompensationMatchedPercentage" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanEmployerContributionParticipantCompensationMatchedPercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanEmployerContributionParticipantCompensationMatchedPercentage" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanEmployerContributionParticipantCompensationMatchedPercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanStatementOfChangeInNetAssetAvailableForBenefitAbstract_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanStatementOfChangeInNetAssetAvailableForBenefitAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Statement of Change in Net Asset Available for Benefit [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanStatementOfChangeInNetAssetAvailableForBenefitAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanStatementOfChangeInNetAssetAvailableForBenefitAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanStatementOfChangeInNetAssetAvailableForBenefitAbstract" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanStatementOfChangeInNetAssetAvailableForBenefitAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueInputsLevel2Member_019eb1ae-c48c-785b-b3a1-f439ad30ffc5_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel2Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Significant Other Observable Inputs (Level 2)</link:label>
    <link:label id="lab_us-gaap_FairValueInputsLevel2Member_label_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel2Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Inputs, Level 2 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueInputsLevel2Member" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueInputsLevel2Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueInputsLevel2Member" xlink:to="lab_us-gaap_FairValueInputsLevel2Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanFullyBenefitResponsiveInvestmentContractLineItems_019eb1ae-c48c-739c-80b4-674254bba2bf_terseLabel_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanFullyBenefitResponsiveInvestmentContractLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">EBP, Fully Benefit-Responsive Investment Contract [Line Items]</link:label>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanFullyBenefitResponsiveInvestmentContractLineItems_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanFullyBenefitResponsiveInvestmentContractLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Fully Benefit-Responsive Investment Contract [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanFullyBenefitResponsiveInvestmentContractLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanFullyBenefitResponsiveInvestmentContractLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanFullyBenefitResponsiveInvestmentContractLineItems" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanFullyBenefitResponsiveInvestmentContractLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanScheduleOfDelinquentParticipantContributionCorrectedOutsideVfcp_019eb1ae-c48c-7ad2-b7e0-34baaecbfa10_terseLabel_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanScheduleOfDelinquentParticipantContributionCorrectedOutsideVfcp" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Contributions corrected outside VFCP</link:label>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanScheduleOfDelinquentParticipantContributionCorrectedOutsideVfcp_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanScheduleOfDelinquentParticipantContributionCorrectedOutsideVfcp" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Schedule of Delinquent Participant Contribution, Corrected Outside VFCP</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanScheduleOfDelinquentParticipantContributionCorrectedOutsideVfcp" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanScheduleOfDelinquentParticipantContributionCorrectedOutsideVfcp"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanScheduleOfDelinquentParticipantContributionCorrectedOutsideVfcp" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanScheduleOfDelinquentParticipantContributionCorrectedOutsideVfcp" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanTaxStatusTable_019eb1ae-c48c-7221-8832-778910bf2007_terseLabel_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanTaxStatusTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">EBP, Tax Status [Table]</link:label>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanTaxStatusTable_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanTaxStatusTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Tax Status [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanTaxStatusTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanTaxStatusTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanTaxStatusTable" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanTaxStatusTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseDecrease_019eb1ae-c48c-77b5-892b-0f21744b7ca4_totalLabel_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseDecrease" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net increase</link:label>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseDecrease_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseDecrease" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Change in Net Asset Available for Benefit, Increase (Decrease)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseDecrease" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseDecrease"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseDecrease" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseDecrease" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanRelatedPartyAndPartyInInterestTransactionsTextBlock_019eb1ae-c48c-791a-a5dd-b00775a4b11b_terseLabel_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanRelatedPartyAndPartyInInterestTransactionsTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party and Parties-in-Interest Transactions</link:label>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanRelatedPartyAndPartyInInterestTransactionsTextBlock_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanRelatedPartyAndPartyInInterestTransactionsTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Related Party and Party-in-Interest Transactions [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanRelatedPartyAndPartyInInterestTransactionsTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanRelatedPartyAndPartyInInterestTransactionsTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanRelatedPartyAndPartyInInterestTransactionsTextBlock" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanRelatedPartyAndPartyInInterestTransactionsTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanRelatedPartyAndPartyInInterestTransactionsAbstract_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanRelatedPartyAndPartyInInterestTransactionsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Related Party and Party-in-Interest Transactions [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanRelatedPartyAndPartyInInterestTransactionsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanRelatedPartyAndPartyInInterestTransactionsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanRelatedPartyAndPartyInInterestTransactionsAbstract" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanRelatedPartyAndPartyInInterestTransactionsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanAccountingPolicyAbstract_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanAccountingPolicyAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Accounting Policy, Accounting Standard Update, and Change in Accounting Principle [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanAccountingPolicyAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanAccountingPolicyAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanAccountingPolicyAbstract" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanAccountingPolicyAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanReceivable_019eb1ae-c48c-736b-8ede-82dc06fa81a7_totalLabel_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanReceivable" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total receivables</link:label>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanReceivable_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanReceivable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Receivable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanReceivable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanReceivable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanReceivable" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanReceivable" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_EBPAssetHeldForInvestmentParticipantLoanMaturityPeriod_019eb1ae-c48c-7198-9c04-1c99967a4e85_terseLabel_en-US" xlink:label="lab_fbc_EBPAssetHeldForInvestmentParticipantLoanMaturityPeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment, maturity date</link:label>
    <link:label id="lab_fbc_EBPAssetHeldForInvestmentParticipantLoanMaturityPeriod_label_en-US" xlink:label="lab_fbc_EBPAssetHeldForInvestmentParticipantLoanMaturityPeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Asset Held for Investment, Participant Loan, Maturity Period</link:label>
    <link:label id="lab_fbc_EBPAssetHeldForInvestmentParticipantLoanMaturityPeriod_documentation_en-US" xlink:label="lab_fbc_EBPAssetHeldForInvestmentParticipantLoanMaturityPeriod" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">EBP, Asset Held for Investment, Participant Loan, Maturity Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_EBPAssetHeldForInvestmentParticipantLoanMaturityPeriod" xlink:href="fbc-20260610.xsd#fbc_EBPAssetHeldForInvestmentParticipantLoanMaturityPeriod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_EBPAssetHeldForInvestmentParticipantLoanMaturityPeriod" xlink:to="lab_fbc_EBPAssetHeldForInvestmentParticipantLoanMaturityPeriod" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanInvestmentFairValueAbstract_019eb1ae-c48c-7661-9a0c-1187668d5ed1_terseLabel_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanInvestmentFairValueAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investments at Fair Value (Note 3):</link:label>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanInvestmentFairValueAbstract_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanInvestmentFairValueAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Investment, Fair Value [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanInvestmentFairValueAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanInvestmentFairValueAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanInvestmentFairValueAbstract" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanInvestmentFairValueAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitDecreaseForPaymentToParticipant_019eb1ae-c48c-7b87-a7b1-b2e5434d7e17_terseLabel_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitDecreaseForPaymentToParticipant" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Benefits paid to participants</link:label>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitDecreaseForPaymentToParticipant_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitDecreaseForPaymentToParticipant" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Change in Net Asset Available for Benefit, Decrease from Payment to Participant</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitDecreaseForPaymentToParticipant" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitDecreaseForPaymentToParticipant"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitDecreaseForPaymentToParticipant" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitDecreaseForPaymentToParticipant" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseForDividendIncomeOnInvestment_019eb1ae-c48c-74c5-b954-1102e52ccc7e_terseLabel_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseForDividendIncomeOnInvestment" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Dividends on investments</link:label>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseForDividendIncomeOnInvestment_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseForDividendIncomeOnInvestment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Change in Net Asset Available for Benefit, Increase from Dividend Income on Investment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseForDividendIncomeOnInvestment" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseForDividendIncomeOnInvestment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseForDividendIncomeOnInvestment" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseForDividendIncomeOnInvestment" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanScheduleOfDelinquentParticipantContributionTransferredLateToPlan_019eb1ae-c48c-7d90-8916-b601922ba622_terseLabel_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanScheduleOfDelinquentParticipantContributionTransferredLateToPlan" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Late remittance amount</link:label>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanScheduleOfDelinquentParticipantContributionTransferredLateToPlan_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanScheduleOfDelinquentParticipantContributionTransferredLateToPlan" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Schedule of Delinquent Participant Contribution, Transferred Late to Plan</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanScheduleOfDelinquentParticipantContributionTransferredLateToPlan" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanScheduleOfDelinquentParticipantContributionTransferredLateToPlan"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanScheduleOfDelinquentParticipantContributionTransferredLateToPlan" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanScheduleOfDelinquentParticipantContributionTransferredLateToPlan" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanAssetHeldForInvestmentInvestmentExcludingPlanInterestInMasterTrustCurrentValue_019eb1ae-c48c-7985-83d0-c691a5246ad3_terseLabel_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanAssetHeldForInvestmentInvestmentExcludingPlanInterestInMasterTrustCurrentValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Current value</link:label>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanAssetHeldForInvestmentInvestmentExcludingPlanInterestInMasterTrustCurrentValue_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanAssetHeldForInvestmentInvestmentExcludingPlanInterestInMasterTrustCurrentValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Asset Held for Investment, Investment, Excluding Plan Interest in Master Trust, Current Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanAssetHeldForInvestmentInvestmentExcludingPlanInterestInMasterTrustCurrentValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanAssetHeldForInvestmentInvestmentExcludingPlanInterestInMasterTrustCurrentValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanAssetHeldForInvestmentInvestmentExcludingPlanInterestInMasterTrustCurrentValue" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanAssetHeldForInvestmentInvestmentExcludingPlanInterestInMasterTrustCurrentValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain_019eb1ae-c48c-7f83-a2f7-3c950a5a87df_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Hierarchy and NAV [Domain]</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Hierarchy and NAV [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueMeasurementsFairValueHierarchyDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:to="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_EBPNonExemptTransactionsLineItems_019eb1ae-c48c-7b38-8996-a63df9f13776_terseLabel_en-US" xlink:label="lab_fbc_EBPNonExemptTransactionsLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">EBP, Non-Exempt Transactions [Line Items]</link:label>
    <link:label id="lab_fbc_EBPNonExemptTransactionsLineItems_label_en-US" xlink:label="lab_fbc_EBPNonExemptTransactionsLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Non-Exempt Transactions [Line Items]</link:label>
    <link:label id="lab_fbc_EBPNonExemptTransactionsLineItems_documentation_en-US" xlink:label="lab_fbc_EBPNonExemptTransactionsLineItems" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">EBP, Non-Exempt Transactions</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_EBPNonExemptTransactionsLineItems" xlink:href="fbc-20260610.xsd#fbc_EBPNonExemptTransactionsLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_EBPNonExemptTransactionsLineItems" xlink:to="lab_fbc_EBPNonExemptTransactionsLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanStatementOfNetAssetAvailableForBenefitAbstract_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanStatementOfNetAssetAvailableForBenefitAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Statement of Net Asset Available for Benefit [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanStatementOfNetAssetAvailableForBenefitAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanStatementOfNetAssetAvailableForBenefitAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanStatementOfNetAssetAvailableForBenefitAbstract" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanStatementOfNetAssetAvailableForBenefitAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanAccountingPolicyLineItems_019eb1ae-c48c-7acd-879d-beb010ecf70e_terseLabel_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanAccountingPolicyLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">EBP, Accounting Policy [Line Items]</link:label>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanAccountingPolicyLineItems_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanAccountingPolicyLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Accounting Policy [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanAccountingPolicyLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanAccountingPolicyLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanAccountingPolicyLineItems" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanAccountingPolicyLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_EBPEmployeeWithholdingTaxesAmountNotRemitted_019eb1ae-c48c-7505-a7af-c0ed75be3ec2_terseLabel_en-US" xlink:label="lab_fbc_EBPEmployeeWithholdingTaxesAmountNotRemitted" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Employee withholding taxes, amount not remitted</link:label>
    <link:label id="lab_fbc_EBPEmployeeWithholdingTaxesAmountNotRemitted_label_en-US" xlink:label="lab_fbc_EBPEmployeeWithholdingTaxesAmountNotRemitted" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Employee Withholding Taxes, Amount Not Remitted</link:label>
    <link:label id="lab_fbc_EBPEmployeeWithholdingTaxesAmountNotRemitted_documentation_en-US" xlink:label="lab_fbc_EBPEmployeeWithholdingTaxesAmountNotRemitted" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">EBP, Employee Withholding Taxes, Amount Not Remitted</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_EBPEmployeeWithholdingTaxesAmountNotRemitted" xlink:href="fbc-20260610.xsd#fbc_EBPEmployeeWithholdingTaxesAmountNotRemitted"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_EBPEmployeeWithholdingTaxesAmountNotRemitted" xlink:to="lab_fbc_EBPEmployeeWithholdingTaxesAmountNotRemitted" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanTaxStatusAbstract_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanTaxStatusAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Tax Status [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanTaxStatusAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanTaxStatusAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanTaxStatusAbstract" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanTaxStatusAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanEmployerCommonStockFundMember_019eb1ae-c48c-749d-b60f-cfd5a1c54847_terseLabel_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanEmployerCommonStockFundMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common Stock</link:label>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanEmployerCommonStockFundMember_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanEmployerCommonStockFundMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Employer, Common Stock Fund [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanEmployerCommonStockFundMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanEmployerCommonStockFundMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanEmployerCommonStockFundMember" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanEmployerCommonStockFundMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanExpensePolicyTextBlock_019eb1ae-c48c-7307-af27-d498bf053a55_terseLabel_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanExpensePolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Administrative Expenses</link:label>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanExpensePolicyTextBlock_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanExpensePolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Expense [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanExpensePolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanExpensePolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanExpensePolicyTextBlock" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanExpensePolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanAssetHeldForInvestmentParticipantLoanAfterDeemedDistribution_019eb1ae-c48c-7966-895c-56119d7673a2_terseLabel_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanAssetHeldForInvestmentParticipantLoanAfterDeemedDistribution" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Participant loan</link:label>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanAssetHeldForInvestmentParticipantLoanAfterDeemedDistribution_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanAssetHeldForInvestmentParticipantLoanAfterDeemedDistribution" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Asset Held for Investment, Participant Loan, after Deemed Distribution</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanAssetHeldForInvestmentParticipantLoanAfterDeemedDistribution" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanAssetHeldForInvestmentParticipantLoanAfterDeemedDistribution"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanAssetHeldForInvestmentParticipantLoanAfterDeemedDistribution" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanAssetHeldForInvestmentParticipantLoanAfterDeemedDistribution" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanInvestmentPolicyTextBlock_019eb1ae-c48c-7be8-a185-98dbf179ef85_terseLabel_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanInvestmentPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment Valuation and Income Recognition</link:label>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanInvestmentPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanInvestmentPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Investment [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanInvestmentPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanInvestmentPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanInvestmentPolicyTextBlock" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanInvestmentPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentType_019eb1ae-c48c-74ff-a052-a8695ba5c1fb_terseLabel_en-US" xlink:label="lab_dei_DocumentType" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Type</link:label>
    <link:label id="lab_dei_DocumentType_label_en-US" xlink:label="lab_dei_DocumentType" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Type</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentType" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentType"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentType" xlink:to="lab_dei_DocumentType" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanPlanTerminationTextBlock_019eb1ae-c48c-7872-b67b-7c24c09e3c1b_terseLabel_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanPlanTerminationTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Plan Termination</link:label>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanPlanTerminationTextBlock_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanPlanTerminationTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Plan Termination [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanPlanTerminationTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanPlanTerminationTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanPlanTerminationTextBlock" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanPlanTerminationTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityCentralIndexKey_019eb1ae-c48c-7d40-8ff7-270abee8a28b_terseLabel_en-US" xlink:label="lab_dei_EntityCentralIndexKey" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Central Index Key</link:label>
    <link:label id="lab_dei_EntityCentralIndexKey_label_en-US" xlink:label="lab_dei_EntityCentralIndexKey" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Central Index Key</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityCentralIndexKey" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityCentralIndexKey"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityCentralIndexKey" xlink:to="lab_dei_EntityCentralIndexKey" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_EBPRiskAndUncertaintyConcentrationOfInvestmentInEmployerStockFundPercentage_019eb1ae-c48c-70ff-843b-40b478b99224_terseLabel_en-US" xlink:label="lab_fbc_EBPRiskAndUncertaintyConcentrationOfInvestmentInEmployerStockFundPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Percentage of plan net assets invested</link:label>
    <link:label id="lab_fbc_EBPRiskAndUncertaintyConcentrationOfInvestmentInEmployerStockFundPercentage_label_en-US" xlink:label="lab_fbc_EBPRiskAndUncertaintyConcentrationOfInvestmentInEmployerStockFundPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Risk And Uncertainty, Concentration Of Investment In Employer Stock Fund, Percentage</link:label>
    <link:label id="lab_fbc_EBPRiskAndUncertaintyConcentrationOfInvestmentInEmployerStockFundPercentage_documentation_en-US" xlink:label="lab_fbc_EBPRiskAndUncertaintyConcentrationOfInvestmentInEmployerStockFundPercentage" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">EBP, Risk And Uncertainty, Concentration Of Investment In Employer Stock Fund, Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_EBPRiskAndUncertaintyConcentrationOfInvestmentInEmployerStockFundPercentage" xlink:href="fbc-20260610.xsd#fbc_EBPRiskAndUncertaintyConcentrationOfInvestmentInEmployerStockFundPercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_EBPRiskAndUncertaintyConcentrationOfInvestmentInEmployerStockFundPercentage" xlink:to="lab_fbc_EBPRiskAndUncertaintyConcentrationOfInvestmentInEmployerStockFundPercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanParticipantLoanInterestRate_019eb1ae-c48c-7de9-99a7-cb806021147f_terseLabel_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanParticipantLoanInterestRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Asset held for investment, participant loan, interest rate</link:label>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanParticipantLoanInterestRate_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanParticipantLoanInterestRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Asset Held for Investment, Participant Loan, Interest Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanParticipantLoanInterestRate" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanParticipantLoanInterestRate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanParticipantLoanInterestRate" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanParticipantLoanInterestRate" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_EBPNoteReceivableFromParticipantGeneralLoanMaximumBorrowingTerm_019eb1ae-c48c-7516-9796-a6744a57c8d3_terseLabel_en-US" xlink:label="lab_fbc_EBPNoteReceivableFromParticipantGeneralLoanMaximumBorrowingTerm" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">General loan, borrowing term</link:label>
    <link:label id="lab_fbc_EBPNoteReceivableFromParticipantGeneralLoanMaximumBorrowingTerm_label_en-US" xlink:label="lab_fbc_EBPNoteReceivableFromParticipantGeneralLoanMaximumBorrowingTerm" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Note Receivable From Participant, General Loan, Maximum Borrowing Term</link:label>
    <link:label id="lab_fbc_EBPNoteReceivableFromParticipantGeneralLoanMaximumBorrowingTerm_documentation_en-US" xlink:label="lab_fbc_EBPNoteReceivableFromParticipantGeneralLoanMaximumBorrowingTerm" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">EBP, Note Receivable From Participant, General Loan, Maximum Borrowing Term</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_EBPNoteReceivableFromParticipantGeneralLoanMaximumBorrowingTerm" xlink:href="fbc-20260610.xsd#fbc_EBPNoteReceivableFromParticipantGeneralLoanMaximumBorrowingTerm"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_EBPNoteReceivableFromParticipantGeneralLoanMaximumBorrowingTerm" xlink:to="lab_fbc_EBPNoteReceivableFromParticipantGeneralLoanMaximumBorrowingTerm" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DefinedBenefitPlanCommonCollectiveTrustMember_019eb1ae-c48c-7531-bdda-4cd406c3da59_terseLabel_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanCommonCollectiveTrustMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Collective Trust Funds</link:label>
    <link:label id="lab_us-gaap_DefinedBenefitPlanCommonCollectiveTrustMember_label_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanCommonCollectiveTrustMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Collective Trust [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DefinedBenefitPlanCommonCollectiveTrustMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DefinedBenefitPlanCommonCollectiveTrustMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DefinedBenefitPlanCommonCollectiveTrustMember" xlink:to="lab_us-gaap_DefinedBenefitPlanCommonCollectiveTrustMember" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_EBPRequisiteServicePeriodDomain_019eb1ae-c48c-7b84-ab48-f24f9f9e84e7_terseLabel_en-US" xlink:label="lab_fbc_EBPRequisiteServicePeriodDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">EBP, Requisite Service Period [Domain]</link:label>
    <link:label id="lab_fbc_EBPRequisiteServicePeriodDomain_label_en-US" xlink:label="lab_fbc_EBPRequisiteServicePeriodDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Requisite Service Period [Domain]</link:label>
    <link:label id="lab_fbc_EBPRequisiteServicePeriodDomain_documentation_en-US" xlink:label="lab_fbc_EBPRequisiteServicePeriodDomain" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">EBP, Requisite Service Period [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_EBPRequisiteServicePeriodDomain" xlink:href="fbc-20260610.xsd#fbc_EBPRequisiteServicePeriodDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_EBPRequisiteServicePeriodDomain" xlink:to="lab_fbc_EBPRequisiteServicePeriodDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanNetAssetAvailableForBenefitAbstract_019eb1ae-c48c-7324-984e-62c7cd9e2bc5_terseLabel_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanNetAssetAvailableForBenefitAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net assets available for plan benefits at:</link:label>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanNetAssetAvailableForBenefitAbstract_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanNetAssetAvailableForBenefitAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Net Asset Available for Benefit [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanNetAssetAvailableForBenefitAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanNetAssetAvailableForBenefitAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanNetAssetAvailableForBenefitAbstract" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanNetAssetAvailableForBenefitAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanTaxStatusLineItems_019eb1ae-c48c-7579-8708-998525a2bc27_terseLabel_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanTaxStatusLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">EBP, Tax Status [Line Items]</link:label>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanTaxStatusLineItems_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanTaxStatusLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Tax Status [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanTaxStatusLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanTaxStatusLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanTaxStatusLineItems" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanTaxStatusLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EbpRiskAndUncertaintyAbstract_label_en-US" xlink:label="lab_us-gaap-ebp_EbpRiskAndUncertaintyAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Risk and Uncertainty [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EbpRiskAndUncertaintyAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EbpRiskAndUncertaintyAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EbpRiskAndUncertaintyAbstract" xlink:to="lab_us-gaap-ebp_EbpRiskAndUncertaintyAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_EBPNonExemptTransactionsTextBlock_019eb1ae-c48c-720d-80a2-d517e37fdad7_terseLabel_en-US" xlink:label="lab_fbc_EBPNonExemptTransactionsTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">EBP, Non-Exempt Transactions [Text Block]</link:label>
    <link:label id="lab_fbc_EBPNonExemptTransactionsTextBlock_label_en-US" xlink:label="lab_fbc_EBPNonExemptTransactionsTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Non-Exempt Transactions [Text Block]</link:label>
    <link:label id="lab_fbc_EBPNonExemptTransactionsTextBlock_documentation_en-US" xlink:label="lab_fbc_EBPNonExemptTransactionsTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">EBP, Non-Exempt Transactions</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_EBPNonExemptTransactionsTextBlock" xlink:href="fbc-20260610.xsd#fbc_EBPNonExemptTransactionsTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_EBPNonExemptTransactionsTextBlock" xlink:to="lab_fbc_EBPNonExemptTransactionsTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EbpSubsequentEventTable_019eb1ae-c48c-762e-8b02-d4970cbcef90_terseLabel_en-US" xlink:label="lab_us-gaap-ebp_EbpSubsequentEventTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">EBP, Subsequent Event [Table]</link:label>
    <link:label id="lab_us-gaap-ebp_EbpSubsequentEventTable_label_en-US" xlink:label="lab_us-gaap-ebp_EbpSubsequentEventTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Subsequent Event [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EbpSubsequentEventTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EbpSubsequentEventTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EbpSubsequentEventTable" xlink:to="lab_us-gaap-ebp_EbpSubsequentEventTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitDecreaseAbstract_019eb1ae-c48c-7fe4-87cf-807e3f3a606d_terseLabel_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitDecreaseAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deductions from net assets attributed to:</link:label>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitDecreaseAbstract_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitDecreaseAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Change in Net Asset Available for Benefit, Decrease [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitDecreaseAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitDecreaseAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitDecreaseAbstract" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitDecreaseAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanForfeitedNonvestedAccountDecreaseForEmployerContribution_019eb1ae-c48c-7daf-a9a1-af8ae91236c4_terseLabel_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanForfeitedNonvestedAccountDecreaseForEmployerContribution" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forfeited nonvested account, decrease from employer contribution</link:label>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanForfeitedNonvestedAccountDecreaseForEmployerContribution_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanForfeitedNonvestedAccountDecreaseForEmployerContribution" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Forfeited Nonvested Account, Decrease from Employer Contribution</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanForfeitedNonvestedAccountDecreaseForEmployerContribution" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanForfeitedNonvestedAccountDecreaseForEmployerContribution"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanForfeitedNonvestedAccountDecreaseForEmployerContribution" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanForfeitedNonvestedAccountDecreaseForEmployerContribution" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_EBPPlanTerminationLineItems_019eb1ae-c48c-75b7-9f88-92ba48a94b9a_terseLabel_en-US" xlink:label="lab_fbc_EBPPlanTerminationLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">EBP, Plan Termination [Line Items]</link:label>
    <link:label id="lab_fbc_EBPPlanTerminationLineItems_label_en-US" xlink:label="lab_fbc_EBPPlanTerminationLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Plan Termination [Line Items]</link:label>
    <link:label id="lab_fbc_EBPPlanTerminationLineItems_documentation_en-US" xlink:label="lab_fbc_EBPPlanTerminationLineItems" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">EBP, Plan Termination</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_EBPPlanTerminationLineItems" xlink:href="fbc-20260610.xsd#fbc_EBPPlanTerminationLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_EBPPlanTerminationLineItems" xlink:to="lab_fbc_EBPPlanTerminationLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanNoteReceivableFromParticipant_019eb1ae-c48c-7520-b1f1-ce116eddc426_terseLabel_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanNoteReceivableFromParticipant" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Notes receivable from participants</link:label>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanNoteReceivableFromParticipant_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanNoteReceivableFromParticipant" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Note Receivable from Participant</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanNoteReceivableFromParticipant" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanNoteReceivableFromParticipant"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanNoteReceivableFromParticipant" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanNoteReceivableFromParticipant" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_VariableAnnuityMember_019eb1ae-c48c-772e-815d-c9e3b20acfab_terseLabel_en-US" xlink:label="lab_us-gaap_VariableAnnuityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Variable Annuities</link:label>
    <link:label id="lab_us-gaap_VariableAnnuityMember_label_en-US" xlink:label="lab_us-gaap_VariableAnnuityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Variable Annuity [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_VariableAnnuityMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_VariableAnnuityMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_VariableAnnuityMember" xlink:to="lab_us-gaap_VariableAnnuityMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis_019eb1ae-c48c-7aed-8594-738f3011d448_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Hierarchy and NAV [Axis]</link:label>
    <link:label id="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis_label_en-US" xlink:label="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Hierarchy and NAV [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueByFairValueHierarchyLevelAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:to="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanSummaryOfAccountingPolicyTextBlock_019eb1ae-c48c-70dd-a2dc-3abff1b829a1_terseLabel_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanSummaryOfAccountingPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Summary of Significant Accounting Policies</link:label>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanSummaryOfAccountingPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanSummaryOfAccountingPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Summary of Accounting Policy [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanSummaryOfAccountingPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanSummaryOfAccountingPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanSummaryOfAccountingPolicyTextBlock" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanSummaryOfAccountingPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityRegistrantName_019eb1ae-c48c-7ec3-a2f7-f26628493413_terseLabel_en-US" xlink:label="lab_dei_EntityRegistrantName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Registrant Name</link:label>
    <link:label id="lab_dei_EntityRegistrantName_label_en-US" xlink:label="lab_dei_EntityRegistrantName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Registrant Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityRegistrantName" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityRegistrantName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityRegistrantName" xlink:to="lab_dei_EntityRegistrantName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EbpSubsequentEventAbstract_label_en-US" xlink:label="lab_us-gaap-ebp_EbpSubsequentEventAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Subsequent Event [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EbpSubsequentEventAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EbpSubsequentEventAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EbpSubsequentEventAbstract" xlink:to="lab_us-gaap-ebp_EbpSubsequentEventAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanSubsequentEventTextBlock_019eb1ae-c48c-71de-ba0e-c84ba3264d30_terseLabel_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanSubsequentEventTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsequent Events</link:label>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanSubsequentEventTextBlock_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanSubsequentEventTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Subsequent Event [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanSubsequentEventTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanSubsequentEventTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanSubsequentEventTextBlock" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanSubsequentEventTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanScheduleOfDelinquentParticipantContributionTableTextBlock_019eb1ae-c48c-7f69-8547-4d97d949d7cb_terseLabel_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanScheduleOfDelinquentParticipantContributionTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule H, Line 4a - Schedule of Delinquent Participant Contribution</link:label>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanScheduleOfDelinquentParticipantContributionTableTextBlock_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanScheduleOfDelinquentParticipantContributionTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Schedule of Delinquent Participant Contribution [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanScheduleOfDelinquentParticipantContributionTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanScheduleOfDelinquentParticipantContributionTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanScheduleOfDelinquentParticipantContributionTableTextBlock" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanScheduleOfDelinquentParticipantContributionTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanScheduleOfDelinquentParticipantContributionTable_019eb1ae-c48c-74fa-9797-28284f75b32a_terseLabel_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanScheduleOfDelinquentParticipantContributionTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">EBP, Schedule of Delinquent Participant Contribution [Table]</link:label>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanScheduleOfDelinquentParticipantContributionTable_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanScheduleOfDelinquentParticipantContributionTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Schedule of Delinquent Participant Contribution [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanScheduleOfDelinquentParticipantContributionTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanScheduleOfDelinquentParticipantContributionTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanScheduleOfDelinquentParticipantContributionTable" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanScheduleOfDelinquentParticipantContributionTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanTaxStatusTextBlock_019eb1ae-c48c-70c1-b72f-805d03dd867a_terseLabel_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanTaxStatusTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income Tax Status</link:label>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanTaxStatusTextBlock_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanTaxStatusTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Tax Status [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanTaxStatusTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanTaxStatusTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanTaxStatusTextBlock" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanTaxStatusTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanNoteReceivableFromParticipantAccountMaximumBorrowingToTotalAccountPercentage_019eb1ae-c48c-7906-8d73-f221f34caebb_terseLabel_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanNoteReceivableFromParticipantAccountMaximumBorrowingToTotalAccountPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Note receivable from participant, account, maximum borrowing, to total account, percentage</link:label>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanNoteReceivableFromParticipantAccountMaximumBorrowingToTotalAccountPercentage_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanNoteReceivableFromParticipantAccountMaximumBorrowingToTotalAccountPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Note Receivable from Participant, Account, Maximum Borrowing, to Total Account, Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanNoteReceivableFromParticipantAccountMaximumBorrowingToTotalAccountPercentage" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanNoteReceivableFromParticipantAccountMaximumBorrowingToTotalAccountPercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanNoteReceivableFromParticipantAccountMaximumBorrowingToTotalAccountPercentage" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanNoteReceivableFromParticipantAccountMaximumBorrowingToTotalAccountPercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_EBP004Member_019eb1ae-c48c-7aa4-8992-9fb11affd19c_terseLabel_en-US" xlink:label="lab_fbc_EBP004Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">EBP 004</link:label>
    <link:label id="lab_fbc_EBP004Member_label_en-US" xlink:label="lab_fbc_EBP004Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP 004 [Member]</link:label>
    <link:label id="lab_fbc_EBP004Member_documentation_en-US" xlink:label="lab_fbc_EBP004Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">EBP 004</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_EBP004Member" xlink:href="fbc-20260610.xsd#fbc_EBP004Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_EBP004Member" xlink:to="lab_fbc_EBP004Member" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentInformationTable_019eb1ae-c48c-7f24-8003-eb711741701d_terseLabel_en-US" xlink:label="lab_dei_DocumentInformationTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Information [Table]</link:label>
    <link:label id="lab_dei_DocumentInformationTable_label_en-US" xlink:label="lab_dei_DocumentInformationTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Information [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentInformationTable" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentInformationTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentInformationTable" xlink:to="lab_dei_DocumentInformationTable" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_EBPLessThanOneYearMember_019eb1ae-c48c-7ae6-98a2-b1174e54bb64_terseLabel_en-US" xlink:label="lab_fbc_EBPLessThanOneYearMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Less than 1 year</link:label>
    <link:label id="lab_fbc_EBPLessThanOneYearMember_label_en-US" xlink:label="lab_fbc_EBPLessThanOneYearMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Less Than One Year [Member]</link:label>
    <link:label id="lab_fbc_EBPLessThanOneYearMember_documentation_en-US" xlink:label="lab_fbc_EBPLessThanOneYearMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">EBP, Less Than One Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_EBPLessThanOneYearMember" xlink:href="fbc-20260610.xsd#fbc_EBPLessThanOneYearMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_EBPLessThanOneYearMember" xlink:to="lab_fbc_EBPLessThanOneYearMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LoanParticipationsAndAssignmentsMember_019eb1ae-c48c-7e29-b4c2-98941e8351a1_terseLabel_en-US" xlink:label="lab_us-gaap_LoanParticipationsAndAssignmentsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Participant loans:</link:label>
    <link:label id="lab_us-gaap_LoanParticipationsAndAssignmentsMember_label_en-US" xlink:label="lab_us-gaap_LoanParticipationsAndAssignmentsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loan Participations and Assignments [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LoanParticipationsAndAssignmentsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LoanParticipationsAndAssignmentsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LoanParticipationsAndAssignmentsMember" xlink:to="lab_us-gaap_LoanParticipationsAndAssignmentsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanNoteReceivableFromParticipantPolicyTextBlock_019eb1ae-c48c-7bcb-8dbb-2298669bba76_terseLabel_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanNoteReceivableFromParticipantPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Notes Receivable from Participants</link:label>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanNoteReceivableFromParticipantPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanNoteReceivableFromParticipantPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Note Receivable from Participant [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanNoteReceivableFromParticipantPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanNoteReceivableFromParticipantPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanNoteReceivableFromParticipantPolicyTextBlock" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanNoteReceivableFromParticipantPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseDecreaseForIncomeLossOnInvestment_019eb1ae-c48c-783c-abf3-dfe9ae524b08_totalLabel_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseDecreaseForIncomeLossOnInvestment" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total investment income</link:label>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseDecreaseForIncomeLossOnInvestment_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseDecreaseForIncomeLossOnInvestment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Change in Net Asset Available for Benefit, Increase (Decrease) from Income (Loss) on Investment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseDecreaseForIncomeLossOnInvestment" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseDecreaseForIncomeLossOnInvestment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseDecreaseForIncomeLossOnInvestment" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseDecreaseForIncomeLossOnInvestment" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_EBPEmployerSafeHarborMatchingConributionsTrancheTwoMember_019eb1ae-c48c-748f-b97d-d7524a373663_terseLabel_en-US" xlink:label="lab_fbc_EBPEmployerSafeHarborMatchingConributionsTrancheTwoMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">EBP, Employer Safe Harbor Matching Conributions, Tranche Two</link:label>
    <link:label id="lab_fbc_EBPEmployerSafeHarborMatchingConributionsTrancheTwoMember_label_en-US" xlink:label="lab_fbc_EBPEmployerSafeHarborMatchingConributionsTrancheTwoMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Employer Safe Harbor Matching Conributions, Tranche Two [Member]</link:label>
    <link:label id="lab_fbc_EBPEmployerSafeHarborMatchingConributionsTrancheTwoMember_documentation_en-US" xlink:label="lab_fbc_EBPEmployerSafeHarborMatchingConributionsTrancheTwoMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">EBP, Employer Safe Harbor Matching Conributions, Tranche Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_EBPEmployerSafeHarborMatchingConributionsTrancheTwoMember" xlink:href="fbc-20260610.xsd#fbc_EBPEmployerSafeHarborMatchingConributionsTrancheTwoMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_EBPEmployerSafeHarborMatchingConributionsTrancheTwoMember" xlink:to="lab_fbc_EBPEmployerSafeHarborMatchingConributionsTrancheTwoMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanRelatedPartyAndPartyInInterestTransactionsLineItems_019eb1ae-c48c-794d-b118-467dd345c067_terseLabel_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanRelatedPartyAndPartyInInterestTransactionsLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">EBP, Related Party and Party-in-Interest Transactions [Line Items]</link:label>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanRelatedPartyAndPartyInInterestTransactionsLineItems_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanRelatedPartyAndPartyInInterestTransactionsLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Related Party and Party-in-Interest Transactions [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanRelatedPartyAndPartyInInterestTransactionsLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanRelatedPartyAndPartyInInterestTransactionsLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanRelatedPartyAndPartyInInterestTransactionsLineItems" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanRelatedPartyAndPartyInInterestTransactionsLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueInputsLevel3Member_019eb1ae-c48c-7402-aa5b-3396c8d2c50c_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel3Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Significant Unobservable Inputs (Level 3)</link:label>
    <link:label id="lab_us-gaap_FairValueInputsLevel3Member_label_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel3Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Inputs, Level 3 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueInputsLevel3Member" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueInputsLevel3Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueInputsLevel3Member" xlink:to="lab_us-gaap_FairValueInputsLevel3Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanScheduleOfDelinquentParticipantContributionNotCorrected_019eb1ae-c48c-7c3b-8875-9c0d28d7a2e2_terseLabel_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanScheduleOfDelinquentParticipantContributionNotCorrected" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Contributions not corrected</link:label>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanScheduleOfDelinquentParticipantContributionNotCorrected_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanScheduleOfDelinquentParticipantContributionNotCorrected" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Schedule of Delinquent Participant Contribution, Not Corrected</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanScheduleOfDelinquentParticipantContributionNotCorrected" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanScheduleOfDelinquentParticipantContributionNotCorrected"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanScheduleOfDelinquentParticipantContributionNotCorrected" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanScheduleOfDelinquentParticipantContributionNotCorrected" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanNetAssetAvailableForBenefit_019eb1ae-c48c-7981-8106-c8f5b3c8c7b8_totalLabel_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanNetAssetAvailableForBenefit" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net assets available for plan benefits</link:label>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanNetAssetAvailableForBenefit_019eb1ae-c48c-7061-8cc7-22be5a726564_periodStartLabel_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanNetAssetAvailableForBenefit" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Beginning of year</link:label>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanNetAssetAvailableForBenefit_019eb1ae-c48c-7fa8-83c4-22d7cd7ec9cc_periodEndLabel_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanNetAssetAvailableForBenefit" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">End of year</link:label>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanNetAssetAvailableForBenefit_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanNetAssetAvailableForBenefit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Net Asset Available for Benefit</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanNetAssetAvailableForBenefit" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanNetAssetAvailableForBenefit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanNetAssetAvailableForBenefit" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanNetAssetAvailableForBenefit" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityDomain_019eb1ae-c48c-7e60-93c9-0a770dbebb89_terseLabel_en-US" xlink:label="lab_dei_EntityDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity [Domain]</link:label>
    <link:label id="lab_dei_EntityDomain_label_en-US" xlink:label="lab_dei_EntityDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityDomain" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityDomain" xlink:to="lab_dei_EntityDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseForContributionAbstract_019eb1ae-c48c-7734-8817-96d102476f1d_terseLabel_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseForContributionAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Contributions:</link:label>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseForContributionAbstract_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseForContributionAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Change in Net Asset Available for Benefit, Increase from Contribution [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseForContributionAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseForContributionAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseForContributionAbstract" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseForContributionAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanForfeitedNonvestedAccount_019eb1ae-c48c-7d41-adbf-8eba6a4200eb_terseLabel_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanForfeitedNonvestedAccount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forfeited nonvested account</link:label>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanForfeitedNonvestedAccount_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanForfeitedNonvestedAccount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Forfeited Nonvested Account</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanForfeitedNonvestedAccount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanForfeitedNonvestedAccount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanForfeitedNonvestedAccount" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanForfeitedNonvestedAccount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanEmployerContributionMatchingPercentage_019eb1ae-c48c-7d2e-8e42-1cbd532cbff3_terseLabel_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanEmployerContributionMatchingPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Matching percentage</link:label>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanEmployerContributionMatchingPercentage_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanEmployerContributionMatchingPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Employer Contribution, Matching Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanEmployerContributionMatchingPercentage" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanEmployerContributionMatchingPercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanEmployerContributionMatchingPercentage" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanEmployerContributionMatchingPercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanStatementOfNetAssetAvailableForBenefitLineItems_019eb1ae-c48c-7335-a08a-612d939c98c7_terseLabel_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanStatementOfNetAssetAvailableForBenefitLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">EBP, Statement of Net Asset Available for Benefit [Line Items]</link:label>
    <link:label id="lab_us-gaap-ebp_EmployeeBenefitPlanStatementOfNetAssetAvailableForBenefitLineItems_label_en-US" xlink:label="lab_us-gaap-ebp_EmployeeBenefitPlanStatementOfNetAssetAvailableForBenefitLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EBP, Statement of Net Asset Available for Benefit [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap-ebp_EmployeeBenefitPlanStatementOfNetAssetAvailableForBenefitLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/ebp/elts/us-gaap-ebp-2026.xsd#us-gaap-ebp_EmployeeBenefitPlanStatementOfNetAssetAvailableForBenefitLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap-ebp_EmployeeBenefitPlanStatementOfNetAssetAvailableForBenefitLineItems" xlink:to="lab_us-gaap-ebp_EmployeeBenefitPlanStatementOfNetAssetAvailableForBenefitLineItems" xlink:type="arc" order="1"/>
  </link:labelLink>
</link:linkbase>
