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I'm sorry to hear about your situation, and my condolences on your loss. You have no obligation for any debts that were in the name of the LLC only, nor any personal liability for debts that he incurred in his name. You would only have personal liability for debts that you personally guaranteed or co-signed for.
Now if he guaranteed the debts of the LLC (rather than just signing them in the name of the LLC) then the creditors could have a claim against his estate. Basically it would be a claim against the amount of money / assets that he would have a claim to (roughly half) of the marital assets. But you still would not have any personal liability to pay those debts. If his estate couldn't cover the amounts owed (again, assuming that he personally guaranteed them) then you wouldn't have to pay the difference. You would have no liability on them whatsoever.
Hope that clears things up a bit. If you have any other questions, please let me know. If not, and you have not yet, please rate my answer AND press the "submit" button, if applicable.
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Thank you, ***** ***** luck to you!