Though state laws and insurance companies' guidelines and policy terms vary normally if your insurance claim for the stolen vehicle was finalized before the vehicle is recovered then you would keep the settlement for the actual cash value (ACV) of the car and the insurance company would take possession of the vehicle.

Usually as part of the settlement process you sign over your title of the stolen vehicle to the insurance company so that in the event the car is recovered by law enforcement they will then be able to take possession and sell it at an auction, etc to recoup the monies they paid out to you for the settlement of your comprehensive claim.

If the car is not badly damaged and you wish to have it back then you could discuss with your insurance company's claim department or insurance adjuster if it is possible to buy back the vehicle from them for salvage value. Keep in mind that usually the car would have to have a branded title of salvage since it was totaled out from being stolen.

You can ask your agent or claims adjuster more about your situation and also get consumer advice from your state's insurance regulatory body.