No, the heirs of a deceased borrower - including a spouse who is not a co-borrower - are not responsible for paying back the loan. Reverse mortgages are non-recourse loans, meaning that even if their balance is more than the appraised value of the home, the extra cost gets absorbed by the Federal Housing Administration.
Still, reverse mortgage rules and regulations put a lot of responsibility on heirs after the death of the last borrower. That is when the reverse mortgage loan comes due and heirs have to decide what to do next. They will usually get 30 days’ notice from the lender to buy the home, sell the home, or turn it over to the lender to satisfy the debt.
It is possible to extend this up to a year so the heirs can have more time to sell the home or provide finances for purchasing it, but the most common extensions are up to 90 days.