In Alabama, the statute of limitations
for personal injury
is only two years. An action against your son wouldn't start to run until his 18th birthday, but they're not suing your son - they're suing you. Initially, that means you can file an Answer defending the case based on the fact that the statute of limitations has expired. Ala Code, Section 6-2-38
If they can somehow establish a basis for extending the statute of limitations, then you do have the option of trying to enter a settlement where you make monthly payments. To win at trial, they have to show that you knew or had reason to know that your son was likely to use the car in a manner that presented an unreasonable risk of harm because of his age. It's hard to argue that a parent should know that all 17 year olds are not fit to drive, because the law has set the driving
age to allow him to drive. There would have to be some other evidence that he wasn't fit to drive, unless he was unlicensed and you gave him the car, anyway. A parent is not automatically liable for accidents caused by a child.
Also, if they do manage to get a judgment (which is not certain at all), then you have the option of filing for bankruptcy to discharge it. It will hurt your credit, but so will a judgment. A judgment would also allow them to garnish a portion of your wages and bankruptcy can help avoid that. If you own a home, there are ways to help protect it.
The short answer is that, yes, you can try to negotiate payment arrangements with them. Some people also might be willing to accept a lesser amount if you can pay upfront, rather than small payments stretched over several years. But you may want to consider some of the other options I mentioned before attempting to work out a resolution with them. A person should not admit liability or agree to pay any debt after the statute of limitations has expired.