If it is a foreclosure auction, it may not sell to an investor but the bank will buy it back at the foreclosure auction therefore taking ownership once the foreclosure deed is filed. They will then assign it to an asset management company to manage the sale which will assign it to an approved listing agent to sell it.
It depends. What sort of auction are you referring to? If it's a bank auction, they'll just list the house until it's sold. If it's a secondary auction, they'll just bring it back up again for the next auction. If it's a trustee auction, it'll go back to the bank.