It appears the cost of repairing the vehicle is not enough to make your insurance company declare the car as a total loss. Due to this, what will happen is that a check will be made out so that the vehicle can be repaired. This will be a claim under your comprehensive coverage since the car was stolen, so a deductible will be owed.

Since you do not own the car outright the check will likely be made out to you and the repair shop or you and the lien holder. The financial institute that provides a loan for a car normally will require that the vehicle be repaired since that is where their interests lie - in their asset, the car.

As for the GAP insurance, it would be unlikely that it would be able to be used in the scenario that you gave. GAP insurance terms may differ so you can check over your specific policy, but typically GAP insurance comes into play only once a vehicle is found to be a total loss.

GAP insurance usually pays the difference between actual cash value (ACV) calculated by an insurance company after a car is totaled and the balance of the car loan. Since your car was not totaled out and you are not receiving actual cash value for it from the insurance company, your GAP insurance would not as a general rule be in effect.