They can go after the spouse because in most states (maybe all of them) your debts are your spouses debts and vice versa.

I knew a guy in California that was gritting his teeth the entire six month waiting period for a divorce because his soon-to-be ex was maxing out her credit cards, getting more credit cards and maxing those too.

Unfortunately for her the rules change a little once you file for a divorce even if it isn't final.