If you're still holding the bag on an income tax debt your ex-spouse drove up, and particularly if you don’t have the wherewithal to repay it, you might be in luck. It doesn’t matter if the tax bill is a result of an understatement of earnings tax on the return, or if it’s just an underpayment of the tax due at the time--you may have a chance of absolving yourself of the obligation for payment. But you’ll have to fight for it.
The IRS doesn’t care if you've got a valid divorce decree and a marital separation arrangement that declares your ex partner is responsible for all previous taxation liabilities—it simply wants to get paid. The IRS’ attitude is: fight it out with your ex, but we’re coming after you.