If you agreed to split property in the divorce and your husband stops paying for his car what can you do to keep yourself from being charged for it?

The divorce decree has NOTHING to do with the contract between the lender and whomever signed it. IF your name is on the contract, you will be responsible for the balance due until it is paid in full or discharged by B/K. The first thing to TRY is get possession of the car and sell it.