Although mortgage lenders will typically allow borrowers to continue to make payments on a loan after foreclosure, unless a redemption agreement is entered, they have no obligation to do so. Absent the borrower's successfully negotiating some form of forbearance agreement or refinancing, there is no obvious path to keeping the home. They may want to discuss the specifics of their bankruptcy discharge with their bankruptcy lawyer, to make sure that their understanding of the bankruptcy proceeding is complete. (If their mortgage was discharged, on the plus side, they cannot be pursued for any deficiency.)
Their best bet is likely to save their money for a new residence, while staying in the home for as long as they can while they find their new home. If they're lucky they will be offered "cash for keys" at some point in the process, such that they will be given a sum of money to move out on or by an agreed date with the home in acceptable condition.

