If you are just a co-signer, then no. As long as your name is not on the title/registration as a co-owner.

I don't understand how this can happen though. Most car lenders require insurance in case the vehicle is damaged. If the borrower does not have insurance, the lender gets "forced place" insurance which is way more expensive than if you purchased yoour own. And co-signing is a bad idea as you are promising the lender that if your son does not pay then you will pay.

Your son is on the road to making bad decisions and driving without insurance is a bad decision. I don't know what is owed on the car, but I would either get it paid off or refinanced without you co-signing. If your son can't afford to do either, then he needs to have both liability insurance (he is going to need more than the statutory minimum) as well as comprehensive in case the vehicle is damaged some other way.