Cross-posted from my reply to the following TED Conversation: "How does life/death manifest itself in the human brain? Is brain death the ultimate end stage of life?"
There is something to the fact that, to maintain a living state, the brain requires a pattern of oscillatory activity with the power distributed in certain frequency bands according to the type of activity that the brain is engaging in. (See Rhythms of the Brain by G. Buzsáki.) However, even after a massive epileptic seizure, which typically indicates a widespread state of electrical noise, the brain is usually able to recover these baseline rhythms.
I think in persistent vegetative state, the brain has very little normal electrical activity, but still, the activity is non-zero -- and the brain appears able to wake itself in some cases. There are stories of people waking up from PVS after several years. It's also curious that you can keep a person's body alive for a long time after their brain is declared "dead" as long as you keep blood flowing and oxygen and nutrients at the right levels. Personally I think that implies the organism couldn't really be declared dead to start with. I don't think it's possible to accurately declare an organism dead until rigor mortis sets in and its microbiome begins to consume it -- in my opinion, decay and the succumbing to entropy is the only true sign of death -- and these forces are set in motion very quickly once an organism "actually dies".
Note that recent research has shown that administering an intravenous dose of Ritalin to a comatose mouse can cause the mouse to wake up almost instantly. They have yet to start human trials, but this may hold real hope for "rebooting the brain".
How long should we keep a PVS patient alive for though? Is it worth 20 years of stress on the family and untold cost of life support? I don't know, but I would say that we need a better understanding of the types of baseline electrical situations from which the brain is able to reboot before we can authoritatively say we know that a patient is actually "brain dead", i.e. beyond the chance of recovery.