My best-friends mother passed away. She had an estranged husband who's name was not on her bankruptcy that she had been making payments on. She has 3 yrs left on this bankruptcy. What happens now? Does he have to assume the debt or is it forgiven?

Depends on the will and if there is any estate or money in the banks, anything in the estate is normally sold to pay any debt first.

No one assumes a bankruptcy, the bankruptcy was hers alone. If her estranged husband, assume they are still legally married, if he is liable for any of the debt, he was already liable.
A bankrupty on a debt only discharges it for the person filing, it does not destroy or do away with the debt. If another person is also liable for the debt, they can still be held liable, when the other person files bankruptcy. So this death, does not make the estranged husband any more or any less liable.