In a divorce, it is common for the parties to have join debt. While there is a lot of focus on dividing up the assets of a marriage, often, not enough attention gets paid to dividing up the debt of a marriage.
A final divorce decree (or settlement incorporated into a final divorce decree) is a court order. Court orders regarding responsibility for payment of debts and liabilities are effective between you and your former spouse, but do not bind a joint creditor that you and your former spouse share. If you still maintain joint credit cards with your former spouse, the only sure way to protect yourself against liability for further charges is to cancel the credit card.
Your Decree should indicate which party is to assume responsibility for payment of certain debts or obligations. For example, if your former spouse is awarded the marital residence and is ordered to assume full responsibility for the payment of the mortgage (but fails to make the payment), the creditor will most likely look to you for the payment of the mortgage until such time as your former spouse removes your name from the mortgage.