I'm assuming that you mean a sale at an auction. There is usually a minimum "reserve" price required. So if the second offer must be above the reserve. Quite often, the amount due on the loan is more than the reserve, so the auction fails and the property goes back to the lender (usually a bank). Then it is technically a 'REO' property. The lender will then get put the property up for sale and all offers are negotiated.