I don't know for sure about the living together thing, but I do know this:
at least where I live and got my divorce (Washington State), legal separation was the best way to protect myself financially until the divorce was done and overwith. Otherwise, if he bought a car and stopped paying for it and we weren't legally separated, I would be responsible for the payments. And, as you stated, if he got in a DUI and killed somebody, they could come after me. But all that stops once papers are filed for legal separation. It's the best way I know to CYA (cover your a$$) until final agreements can be reached about division of property, parenting agreements, etc. In this situation, CYA is definitely in your best interest...........
Good luck!