The at-fault party's insurance company is only responsible for settling with you for the actual cash value (ACV) of your vehicle. If you owe more than the current value of your car then you will be responsible for paying this difference unless you have GAP insurance.

GAP insurance should pay the difference between the ACV you will receive from the at-fault driver's insurance carrier and the balance of your loan. Without this coverage if you are upside down on your loan, owe more that the worth of your vehicle, then you personally will be held responsible to finish paying off the vehicle to your lien holder after the insurance settlement check has been paid out to them.