What should happen is the house goes for what it's worth, and the bank gains or loses accordingly. But often the bank won't accept less than the outstanding amount.
They might set a starting bid, have a (secret) reserve price, or have the right to submit a final bid if "real" ones are too low. But if the house is worth comfortably more than the 306k remaining on the note, someone will bid at least that much.
Over leveraging yourself on too much house and losing it is dumb. Taking a house you own, pulling out a fraction of the equity, and letting that go to foreclosure is even dumber.