This has a biological element to it, so I have also asked it on Biology SE, but there is an interesting philosophical element as well. What is it that makes us 'alive'? Our heart beat? Our brain functionality? These questions point to the overall question: what makes someone 'dead'?
The standard, biological definition. Living things:
- Are composed of cells
- Have different levels of cellular organization
- Use energy
- Respond to their environment
- Adapt to their environment
While it's not entirely clear whether certain organic molecules (like virii) meet all of these criteria, it's agreed that the overwhelming number of living things share these criteria.
The clinical definition of being dead is:
Cessation of blood circulation and breathing, the two necessary criteria to sustain human and many other organisms' lives
While looking at the 'philosophical' question of whether or not someone is dead might sound interesting, I think what you're actually interested in knowing is under what conditions someone is no longer a conscious person.
Being 'dead' has a very real, and straight-forward answer. Once you die your body will no longer work. If you aren't dead, but unconscious, it is possible that your consciousness can be restored with the right types of therapy.
Lacking consciousness would be caused by very specific conditions in the brain.
Anyway, hope that helps.
The definition of alive is often given as "not dead". Ironically, the definition of dead is often given as "not alive". I got those from a online definition search. Biologist struggle to define those things that are alive. Though most would agree that a squirrel is alive, there is some debate about a virus and a prion really pushes the envelope. The best definition I have found for what is alive is an entity that can acquire "food", metabolize and act. I put food in quotes on food as it may not be what you expect. Plants "eats" sunlight for instance. Given that definition a Human is dead when they can no longer do those things.