If one of the parties does not just give everything to the other, or they do not come to a reasonable agreement, or a pre-marital agreement was not in place, most often you will see a not so nice battle over who is responsible for what debt or debts. Ultimately the judge usually makes the decision after a lengthy negotiation among the parties attorneys. One party will be awarded this and the other will be awarded that but one piece of very important information is usually missed. Just because one party is awarded a debt does not mean the other party is not financially responsible. Maybe they are not legally responsible for the debt, in the eyes of the law, but to the creditor they are financially responsible.
Here is a scenario. Party A is awarded the debt of a joint medical bill. Party B, in the eyes of the court does not have to pay that debt. However the creditor has a contract in place between both parties. The responsible thing for Party A to do is either pay the debt in full or get a small loan to pay the debt off. If Party A does not do either one of those and allows the debt to go into default it will effect Party B. Even if Party B disputes the debt and comes to the table with the divorce decree, the creditor still has the legal right to take adverse action against both parties. In some cases the party that is not awarded the debt will have a stipulation placed in the divorce decree that the other party has a specific amount of time to remove the other party's financial responsibility of that debt. This is most often seen when a home is involved. In the event the debt or debts are not taken care of and the other party is negatively effected, they can take the first party back to court and file suit.
*Note. This is not legal advice and should not be construed as such*