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Are your family members, legal "members" of the LLC? What do the by-laws say about the members and who owns what?
You made up the company, so make up a set of by laws that says, "when one member dies, the ownership of his/her portion of the LLC will transfer to XXXXX XXXXX and XXXXX XXXXX. End of story. When you make up a company, you make the rules. How often you get paid, where you are located, what the name of the company is, what you sell or the service you provide, etc. etc. You can also decide what to do with the shares of a member who dies. Please feel free to ask any follow up questions.