When a lender forecloses on a property, it goes to auction. At the auction there will either be a bidder who pays more than the amount of the lender’s lien, or the lender will bid the lien amount and take a deed to the property itself. At that point, the property becomes part of the lender’s REO inventory.
To answer your question, consider the following example: the lender is owed $100,000 for a property and at the auction someone bids the default amount, plus $1,000. At the same time, the lender has another property that no one bids on. The lender bids the $100,000 lien amount and takes the property back into its inventory. Let’s assume for the purpose of this illustration that both homes are exactly the same in every way and are in the same subdivision. Let’s also assume that similar homes are selling for $130,000. Why should the person who bid $101,000 for one property be able to sell the house for $120,000 and and the lender only be able to sell its identical property for the default amount as your question suggests?
My point is that once a lender takes back a property through foreclosure and has the property in its REO inventory, the fact that it is a lender or that it was able to obtain the property for less than what it was worth makes absolutely no difference in terms of what it can sell the property for. What if the bank can’t sell the property for the default amount and has to take less?
The bottom line is that the lender can sell the property for whatever it can get in the marketplace. Sometimes that amount is more than the default amount, sometimes (especially nowadays) that amount is less. As far as where the money goes, the bank gets to keep it… and maybe make up for some of the losses it had to take on other properties where it couldn’t get what it was owed.