Can they suspend my silence if somebody got into an accident in my car?

In 2009 my ex got into a accident in my car it was a third car so was like hit and run so he ended up hitting the other car and the other car that caused the accident ran away and never found till this day and at that time. I didn’t have insurance on my car and the other party have insurance so their insurance made my ex signed some papers and was paying them $50 dollars a month. And later he lost his job and he stopped the payment so they suspended his license couple of months later they also suspended my license so now both our license are suspended. They want me to pay for the accident that my ex caused. Can they do such thing as this?