If the facts are as you have stated - the credit card was solely in the decedent's name, and the debt was "personally" guaranteed, then it is likely that the business is not liable fot the decedent's personal debts on that credit card.
There are several factors, however, which must be considered - did the partner use the card in question for business purchases or expenses? Was it his customary habit to use the card for business expenses? If so, was the card issuer aware of such use? Were the vendors aware of such use.
You may want to consult a local attorney to determine what the partnership liabilities may be with regard to the decedent's outstanding credit account.
You also need to look at the card holder agreement. They often say surprising things, such as anyone who has ever signed a credit card receipt is bound by the agreement and liable for the debt on the card. I am not saying your partner’s agreement had such a provision just check. It is also possible that he put the business on the card as a guarantor, additional card holder or some other relationship; again I hope it is not there but check.
That all depends on who's name the card was or if it was a business credit card. If it was a personal credit card, then the liability remains with his estate. If it was a business credit card wih his name on it, then the liabiliy remains with the business. Business partners usually are not liable especially if the partnership was a limited liability partnership and if the business partner did not give a personal guarantee.