In divorce cases debts come in two flavors: community debts and separate debts.

A community debt is, by and large, any debt created by either or both spouses while they were married.
Community creditors generally look to both spouses to pay community debts, but the creditor is within his rights to ask only one spouse to pay the whole community debt. It is the right of the creditor to demand payment from only one spouse that creates a good deal of confusion for divorced husbands and wives.

One of the divorce court's tasks is to decide and order which community debts each spouse will be responsible to pay. But the divorce court's order affects only the two spouses. The divorce court's order has absolutely no effect on the creditors, who can demand that the other spouse pay the bill if the one the court ordered to pay it fails to do so.
If one spouse ends up paying community debts that the other spouse was ordered to pay, he or she can go back to the divorce court to ask the court to order that they be reimbursed or ask for a judgment against the non-paying spouse and then garnish their wages. If the spouse who was supposed to pay a community debt declares bankruptcy, sometimes there is nothing the other spouse can do but also declare bankruptcy.

The reason creditors are not controlled by divorce court orders is the fact that creditors are not parties to the divorce case. The creditor will have had no voice in the decision of who is to pay what, and it wouldn't be fair for a court to be able to change the rights of someone who wasn't allowed to have their say in the case.
Another common misconception about debts in divorce cases is when one spouse demands the other spouse, "remove my name," from the mortgage or the car loan or the credit cards. It is not within the power of the divorcing spouses or the divorce court to relieve either spouse of their individual responsibility to pay community debts. That power rests in the hands of the creditor, and the creditor is not likely to be foolish enough to remove either spouse's name from the account.

One other common misconception is that by placing an ad in a newspaper, saying you're no longer going to be responsible for anyone's debts but your own, you can magically change community debts into separate debts. It doesn't work that way. Once again, a community debt is, by and large, any debt created by either or both spouses while they are married. People who marry are married until there is a court order that says otherwise, and ads in a newspaper will not change their legal obligations.

Source:AllLaw