Yes, you can sue the at-fault driver, BUT you can't get double recovery, or be paid twice for the same thing. The money going to the finacier counts as money paid to you, since you owe the financier and this is paying off a debt you could otherwise be sued over.When your car is totalled, you can recover the sum of 1) the then-current fair-market or blue book value of the car; 2) any out of pocket cost, like towing the wreck, you incurred; 3) car rental for a reasonable period of time, which is generally around how long it would take someone to get a new car if the had the money for it (since it is not the other driver's fault that you apparently don't have savings, the other driver doesn't have to pay for any delays in getting a new car caused by that)--typically, you can get around 2 or 3 weeks of a rental. Total the above. Subtract from that the amount the insuer is sending to the financier to pay off your debt. You could sue (such as in small claims court) for the balance. You can get instructions and forms from the small claims court (either onine or in person).