Only at the time of a claim, accident, or traffic stop does it often become an issue if you have insured a car that’s not yours. It gets a little tricky if a vehicle has been impounded and the driver has been detained or has a suspended license. You have a couple of options. You can either wait until the owner is free to buy insurance and resolve his driver's license issues, or have him sign over the title and put it in your name. That way, you can buy the insurance and go through the process of getting the release and the car out of impound.