Is there anything else for BIA or the lender to do after BIA makes payment?
Primary source
Verbatim text below is from the Electronic Code of Federal Regulations (eCFR), a public-domain U.S. government work. Always verify the current version with the eCFR before relying on it for any legal matter.
Full Text
When BIA pays the lender on its claim for loss, the lender must sign and deliver to BIA an assignment of rights to its loan agreement with the borrower, in a document acceptable to BIA. Immediately upon payment, BIA is subrogated to all rights of the lender under the loan agreement with the borrower, and must pursue collection efforts against the borrower and any co-maker and guarantor, as required by law.
This is legal information, not legal advice. Laws vary by jurisdiction and change frequently. Always verify current law with official sources and consult a licensed attorney in your jurisdiction for advice on your specific situation.