My response:
Well, that's one scenario. The other can be that the car is ordered to be sold, and the proceeds divided - - if there's anything to "divide"; i.e., if the leinholder has been paid in full. If it is sold, and there remains a deficit owed to the leinholder, each of you will be ordered to incur half of that deficit.
You see, herein lies the problem for you : Since, as you know, California is a Community Property State, and since your "trade-in" car was obviously purchased during the marriage, all assets of the marriage are to be divided equally. So, it makes no difference who "earned" the money for, or how the "trade-in" car was registered, when it was first purchased. The fact remains that it was still an asset of the marriage (in California), and everything shall either be divided or sold.
If, in your Marital Settlement Agreement, he takes on any of the Marital Debts, MAKE ABSOLUTELY SURE that you place a clause in the agreement that neither one of you shall make any such debts included in any Bankruptcy proceeding. Because, if you don't, and if he files for BK, all of the joint or shared debts will become 100% yours.
IAAL