You have filed a legal separation, right? If not, you may still be liable for debts she runs up.
This happened to my son. His XW had credit cards in her name only that he did not even know about. She used them to fund trips with her lovers (their were many) while he was away for military training. A year after he caught and divorced her the debt collectors came after him for payment. He got a lawyer but ended up having to pay them off or let his credit be ruined. Evidently since they were married at the time it did not matter if his name was on the accounts or not.
Getting a legal separation would have avoided that. Think about it.