If your 2000 Honda Civic is stolen by a thief, you would be able to put a claim in with your insurance company through your comprehensive coverage. If your car was not recovered, after an investigation of the claim the insurance company would normally settle with you for the actual cash value (ACV) of the vehicle.

The ACV is basically the worth of the car at the time it was stolen. It is usually calculated using such means as recent local sales of similar condition like model vehicles, blue book, and the insurance companies own internal information.

If the ACV is below the $8K that you own on the vehicle, you will be responsible for the balance of the loan that is owed on the vehicle. If you have GAP insurance it would help by paying the difference between the ACV paid by the comprehensive policy and the loan amount still due.

Payments for your vehicle should still be made until the lien holder would tell you they are not due. Stopping payments, while waiting for the settlement check from the insurance company, could cause problems with your loan and be put on your credit history as late or non payment.

As for the insurance, you would need to speak to the insurance company to see when you could stop payments. You would not want to cancel coverage before the settlement is made, especially because the car might be recovered and thus need the coverage still on it.