Answer:
The account is owned by the entity, the LLC, which did not die and will never have an estate. The LLC remains the owner of the account. The estate of the deceased individual is the owner of the LLC (but not the owner of the account). State law, the documents creating the LLC and the will of the deceased LLC owner will all have something to say about what happens to the LLC, but the bank does nothing except wait for the next act when someone assumes control of the LLC.
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