If the illegal can drive away from an accident he will. Otherwise he will run away. Police won't bother to attempt to find him. He/his car has no insurance. If you are lucky you have insurance to cover most of your car damage. Tough luck about injuries or the deductable. On the other hand think of the money you're saving by having the cheap labor. Think it balances out?
Especially when you consider that illegals annually transfer some $17 billion of their earinings out of the US and into Mexico and Latin America.