The Living Computer Museum wasn't structurally a museum, it was Paul Allen's collection. Part of running a museum includes having a plan in place that the museum will continue running past the death of one particular billionaire. Allen never did this, so when he died the LCM died with him. It would have been trivial for someone of Allen's wealth and status to get one of his lawyers to set up a legal structure with an endowment that would have allowed the museum to continue to operate indefinitely rather than become a part of his estate. For whatever reason, he chose not to do this.
