You would have to pay the balance out of pocket, since the full remaining balance of the loan must be paid regardless of how much you received in settlement. Therefore, unless you had GAP insurance to pay any shortfall for you, you will have to pay that shortfall yourself. You can try to negotiate more, but at the end of the day, they do not have to pay more than the then-current fair market value of the car (what it was worth), even if thati is less than owe.