Debt obligations upon spouse's death

I have been separated from my husband for some years (though it is not a legal separation). My husband's business is at this time deeply in debt. His corporate affairs are a mess and he is possibly personally signed upon some of this debt. My question is whether I can be held liable for any of his debt upon his death.

This is really a bankruptcy question, and there is a lot more I'd have to know to be able to answer. Like the state you are in, when the debts were incurred (when you were living together or after, etc.)