This is a sticky situation in terms of both finances and legality. Because you’re the cosigner and not the co-borrower, you have no legal right to possession of the car. It’s still owned 100% by your former partner. Yet because your ex can’t make the payments, you’re still on the hook for the payments as a cosigner.
Since you can’t afford the payments or get refinancing, your best bet is to obtain a cosigner release from the lender. This document absolves you from liability on car payments and takes your name off the loan. If you’ve made on-time payments in the past, the lender may agree to the release. However, you’ll want to move on this immediately to avoid any late payments in the near future, which can put your release in jeopardy.