I assume that you have a corporate resolution appointing the authorized signer and it sets forth the authorities that the LLC granted that authorized signer. That corporate resolution was appropriately signed by an individual which (at that time) would be allowed to make that representation to the bank according to the corporate documentation.
Just because one or more of the shareholders of the LLC dies, it does not nullify those documents. The fact that there was only one shareholder in this case makes absolutely no difference. The LLC survives on its own, unless the corporate documents indicate that the LLC is immediately dissolved in the event of the death of the shareholder, which I cannot imagine. What the heirs need to do is figure out who is inheriting the stock of the LLC. Otherwise, the LLC just moves on with its business.
If the LLC needed to purchase some materials and you restricted their funds (like you said you did) and the LLC subsequently suffered a financial loss or a loos of profit opportunity, if I was one of the heirs, I would be seeing you in court.
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