As soon as you know you are going to be getting a divorce, immediately cancel all joint accounts.
Regardless of who accumulated the bill, creditors can legally try to collect payment from either party on the joint credit card or other credit account. You will be responsible for payment as long as your name appears on the joint accounts.
The agreement that is reached during the divorce may state who must pay the bills. From the creditor's point of view, both your spouse and you are responsible as long as the joint account stays open. The creditor will attempt to receive payment from who they think are most likely to pay while reporting late payments to the credit bureaus in both names. Due to the irresponsibility of the co-signer, your credit history could be harmed.
You may be required to pay the remaining balance in full upon closure of the account. If this is the case, ask the creditor to distribute the outstanding balance to separate accounts.