The owner of a foreclosed house becomes the bank, or more precisely, whoever the bank sold the bond to. In answer to your question, yes they can hold it, but there are a lot of very complicated reasons not to. They involve liquidity ratios and the like. So selling makes since in a great many instances. In short, what a bank, or financial institution does with it will depend on their fiscal position. Or it SHOULD. This mess has shown us that they can behave irrationally.