Get A lawyer. There is a procedure for bringing a case against a person who has died. It's extra work for the lawyer but you're rights can still be protected. The key in this situation is to act as fast as possible to make sure that the decedents insurance company has been notified that there is a case. Don't try this alone!
You are going to be assigned an attorney by the insurance company. They will handle your case, even though you can hire your own personal attorney at your own expense. Because Fort Wayne has very high quality insurance defense attorneys, you'll probably feel comfortable with the attorney your insurance company hires. Not knowing the injuries, it is difficult to determine the value if the injured person's case. Luckily, you were smart enough to purchase a healthy amount of liability coverage....
They are putting you on the elevator! Get a lawyer right now!!!!! I'm not saying you need to hire me, in fact, don't. But first thing in the morning, get a lawyer and get a lawsuit on file! They won't bargain fairly when your back is against the wall!
A lawsuit needs to be filed immediately!
The reason a good personal injury lawyer is helpful is that the lawyer takes the facts of your case and makes an argument. Here we are missing far too many facts to figure out your case. Talk to a lawyer.
They are responsible. The lack of insurance on your car has nothing to do with fault or damages. Get a police report which have the identity of the other drivers insurance company. You can then contact that insurance company and make a claim for the damages to your car.