Many homeowners who made responsible house purchases but are stuck with homes worth significantly less than they owe have difficulty selling because they either require unavailable up-front cash or a risky short-sale or foreclosure procedure.
A federal loan to owners in good standing for the amount still owed to the bank/lender after a sale allows the owner to move on without a negative credit impact, a buyer access to a home at market rate, the lender to not lose money, and for federal loan revenue. The loan payments are enforced by being tied to a special tax line item. The minimum payments scale proportionally to current income (ex: accelerate payments for richer or even delay them without penalty in case of job loss).