If I purchase the car??
If was in common-law relationship and sign over the car to my other half, but i still have papers stated that i purchase the car and the owner is in this name, can he declare burkruptcy on the car because there is a lien on the car??

First of all it sounds like the car is pledged to the financing company. As such, this loan would survive bankruptcy (if you kept the car). The only way to be cleared from this debt is to give the car back and then file for a bankruptcy. Now, assuming your ex gives the car back to the lending institution and files bankruptcy, the lending institution will go after you for the short fall if you are still listed on the lending documents.