They get stuck with the whole bill.
Your co-signer assumes full liability on your loans when they sign up as a co-signer. Technically, the credit card, bank, credit union, etc., can enforce joint and several liability against you both. This means that either one of you is liable for the whole debt amount.
So, if a car gets repossessed, the bank can sue either one of you for the remaining deficient balance after they sell the car. If you file bankruptcy, you can discharge this debt, but your co-signer hasn’t filed bankruptcy. They are liable for the full amount, and no amount of phone calls or explanations from you will absolve them from that liability. Often, when one co-signer files bankruptcy, it drags the other co-signer into bankruptcy as well as creditors begin to collect against the non-bankruptcy party.
The best solution to this is to never co-sign for anyone on anything. In practice, this doesn’t work. You may decide to co-sign on a car for your live-in girlfriend of the past 4 years, but when she moves out, you’re on the hook. You may co-sign with your husband, but sometimes marriages end. I have filed countless cases where mom and dad have co-signed on a huge new F350 for their son’s fledgling construction business. It happens, and when you go bankrupt, mom and dad are left holding the bag.
There is nothing that prevents you from contacting the bank and making payment arrangements so that the bank does not collect on your co-signer, but you would have to do this after bankruptcy. If you do this before bankruptcy, you are making a pre-petition transfer to a now unsecured creditor, and this is a bad thing.