For the irreversibly-zombified human, libertarian theory tells us that zombies—not being moral actors—cannot own property. This means that any property held by a person becoming irreversibly zombified becomes unowned, and is therefore subject to immediate homesteading by the first comer. So long as no other non-zombified legitimate claimants exist, unlimited expropriation of formerly-just, now-unowned property from zombies is morally defensible. The same is of course true of the material of the zombie's body, leaving open the possibility of the assemblage of a zombie slave army by a sufficiently skilled and motivated propertarian anarchist.
However, what of the new zombie's heirs? As irreversible zombification is not typically provided for in wills (i.e., it's not really "death"), perhaps a variant of a living will could be used to ensure that the zombified's property passes to their regular heirs in the case of such an eventuality. We might call this new legal instrument an "undead will".