Were you properly insured? If so they should handle the claim. If not after a few years you could have a judgment, but this is not a 30 day process. If the car has no equity meaning you owe more than it is worth - it is unlikely that it would ever be taken. However, since I don't know the details of your accident, I would suggest you speak to a local attorney who can determine all the details and give you the best answer.
You have not provided enough information to give you a complete answer. It is possible for a car to be taken if a judgment is entered against you. However, in most cases, it is very unlikely that this would happen.
You should report the claim to your car insurance company and let them handle responding to any claim that is made.
If you have a judgment against you anything you own may be at risk. If you are asking how you can make your car judgment proof--I do not see any way for you to do that.
However, judgment can only occur after a lot of other things have happened. It is not something that takes place over night--and if you had proper and adequate insurance at the time of the accident, chances that a judgment is entered against you is slim--but it can happen and it all depends on the type of the car accident and the injuries and damages that has resulted.
Disclaimer: I am a lawyer licensed in the State of Illinois only, and I am not your lawyer (unless you have been in my office and signed a contract). This communication is not intended as legal advice, and no attorney client relationship results. Please consult your own attorney for legal advice. This is for informational purposes only.