If my parents co sign a car loan for me and my name is the only name on the title?

I believe you're asking whether they are liable if you have a car accident. If that's what you're asking, then the answer is "no" if they are not on the title or registration, depending upon your age. Contact your insurance company and ask them as well. Good luck.

If your name is on the title, it is your car. If someone causes an accident while driving it with your permission, you can be held liable. Your parents can't be held liable because they do not own the car. But, they are liable on the note, so if you don't pay, the bank can go after them.

If you default lender goes after parents. Lender doesn't care who the car is titled to. If all default car gets repossessed.