Yes. The commonly held notion that a bank (or any other lender) must sell a repossessed property for the same amount it cost to gain possession and therefore cannot make a profit is false. If the foreclosing lender is the successful bidder at the auction, it will take possession of the property for the very first time. When this happens, all the rules change. The lender, now the legal property owner, can do anything it wants with the property, Rent it, keep it, whatever. It can also sell the property for any amount it so desires.