Probably, in 30 days or so, they'll give up and let basically anyone claim her body. Now Marsha wanted to be cremated, and I understand that funeral homes in Virginia won't do cremations without a state-approved next of kin. On the other hand, if no one claims the body, eventually the city will step in -- and cremate her.
That's certainly not as horrifying or as stupid as what's happened to some of the living folks denied habeas corpus recently -- say the U.S. decision that certain Guantanamo detainees weren't enemy combatants after all, but that we'd nevertheless keep them locked up for years, then dump them in Albania three days before an appeal was due to be heard. 
But it's still an example of David Graeber's argument that bureaucratic procedures are stupid because they "are invariably ways of managing social situations that are already stupid because they are founded on structural violence." (He defines structural violence in the previous sentence: "What I would like to argue is that situations created by violence—particularly structural violence, by which I mean forms of pervasive social inequality that are ultimately backed up by the threat of physical harm—invariably tend to create the kinds of willful blindness we normally associate with bureaucratic procedures.") 
To unpack that a little further: the folks who dealt with me had no need to figure out why I said I was Marsha's next of kin (companion of twenty-three years or crazed person who crashed her deathbed? who cares?) After all, if I were to convince a bunch of my friends that we should all go get Marsha's body and cremate it ourselves (say), men with guns would show up to prevent us. Since they know I know that, they can be sure I won't in fact make such a nuisance of myself, and they don't have to spend time figuring me out -- they only need to see where I fit on the state's list of candidates for "next of kin", and move on when it works out to "none of the above". As Graeber says, "Bureaucratic procedures are all about questions of definition. Or, to be more precise, they are about the imposition of a narrow range of pre-established schema to a social reality that is, usually, infinitely more complex." 
So what to do? Shout "Come and see the violence inherent in the system"? I suppose that's what this post is; and there's some use in giving an example of how structural violence works. But what do I do next?
I could just shut up, and go on. Or I could become a reformist: Vermont's pre-established schema is slightly wider than Virginia's -- you can set up a living will, appoint a health care agent, appoint someone to make decisions about organ donation, and appoint someone to dispose of your remains, all on the same form. I could spend many happy years, I suppose, trying to make Virginia's system less stupid.
Marsha despised stupidity, and stupid rules particularly. I would like to honor that, and I don't yet know how.
 Hilzoy, "Freedom!". 2006. http://obsidianwings.blogs.com/obsidian_wings/2006/05/freedom.html
 Graeber, David. 2006. "Beyond Power/Knowledge: an Exploration of the Relation of Power, Ignorance and Stupidity" http://www.lse.ac.uk/collections/LSEPublicLecturesAndEvents/pdf/20060525-Graeber.pdf
 Graeber, David. 2007. Possibilities: Essays on Hierarchy, Rebellion, and Desire, p. 404. Oakland, AK Press
 Monty Python and the Holy Grail, Dir. Terry Gilliam and Terry Jones, 1975