If its not your fault, don't sign crap except for endorsing the check they send. However, read that information through as well. I've seen letters with checks that state upon cashing or depositing the check, you agree to all terms of the letter, etc etc
And on vehicle loans, the vehicle is the security on the loan. If there is no vehicle, then there is nothing for the loan company to secure the loan with, therefore they will care. If you owe more than what the other insurance can and will give you after all options are exhausted, your only other course of action is to pay off the loan yourself and take the person responsible for the accident to court. Taking him/her to court works fairly well as they are responsible. courts tend to lean in your favor on that. You can sue and put a lein on his property. If he doesn't have any property, you can put a lein on him for future $$$ he was to ever earn until you are paid. Now I'm sure we aren't talking about hundreds of thousands of dollars, so more than likely the court will put a lein on his house or other cars, etc.
Oh yeah, if he is a homeowner, then he prob. has some personal liability insurance to cover things like this. If he doesn't, hes an idiot...