In many states, you must immediately report an accident to your insurance company. (Most insurance contracts require this.) Failing to report the accident may give the company grounds to defend you in a lawsuit.
So what happens?
Drunk guy hits the OP. The OP feels bad for the guy. Says, "You have enough trouble. We don't have to report this to our insurance companies." Two years later, the OP tells his insurance company he is being sued. His insurance company says: "You didn't report the accident immediately. We are therefore denying coverage."
I can't say that is what happened or that the OP will be denied coverage. But it is something he will need to work out with his insurance company.
What will likely be the OP's saving grace is that the $500 the drunk guy sent him was a FULL settlement of all claims that either party could bring. By paying the $500 to the OP, the drunk guy settled with the OP and also gave up any right he had to sue the OP. So the OP will be able to defend himself by noting that the $500 was a full settlement of all claims.
Now the drunk guy will say that he did not release the OP from future suits and that the $500 was just to pay for the OP's car. But will they take the word of the drunk guy over the OP's?