If your car is stolen and you have Comprehensive coverage than your insurance company should, after their investigation of the claim, pay you actual cash value (ACV) for your vehicle. Actual cash value is the amount your vehicle was worth in the condition it was in before the accident.
You may owe more or less than the ACV settlement amount that your auto insurance company pays out for your stolen vehicle. If you are upside-down on your loan and thus owe more than the car is worth at the time of the theft than you would have to pay any amount over the ACV your insurer pays out for the vehicle.
If instead you owe less than the car is worth, say the car is worth $15,000 and you owe only $12,000, then your insurance settlement should pay off your vehicle loan and give you the money above the loan pay off.
If you owe more than the car is worth and had purchased Gap insurance then this policy should pay the difference between the ACV amount paid out by your insurance carrier and the balance of your loan or lease.
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So if your car is stolen and you have Comprehensive coverage your insurance company will pay out actual cash value for the vehicle. Whether this will pay off the car depends upon what you owe. If it does not pay off the car than you will be responsible to your lien holder to continue to pay off your loan balance unless you have Gap insurance to cover this.
Unfortunately if you only have Liability and not Comprehensive coverage on your vehicle than your insurance company would pay nothing and you would be responsible for paying on a car you no longer had. Lien holders normally require physical damage coverages of Collision and Comprehensive so you should have these coverages on your vehicle until you pay it off. | 
