One theme that's been explored somewhat in popular culture is brain death, and the interesting dynamics of what separates dead from alive.
In chemistry, death is defined as the loss of the ability to control entropy within an organism. The parts that are supposed to be wet become dry, the parts that are supposed to be dry become wet, the parts that are supposed to be at a specific temperature... well, you get the idea.
In medicine, heart rate, respiration rate, blood pressure, EKG, and oxygen saturation are often used to detect death of the body, but none of these measures adequately address brain death in cases like cervical spinal cord injury. Rarely, there will be a patient with a fully functioning brain but loss of function otherwise, a patient who, while perhaps not destined for a particularly high quality of life, is otherwise a fine candidate for a heart or lung transplant, depending on the level and type of injury.
In such cases, where the only reliably functioning or even injured but recoverable organ is the brain, how are patients with otherwise weak or undetectable vital signs, kept on life support, distinguished from those who are well and truly dead?
P.S. For lack of better tags, I used the diagnostics and symptoms tags. I'm not quite sure that I've ever heard spoken the term "symptoms of death", but it does serve its purpose rather well.
P.S. #2 At the suggestion of Carey Gregory, a little clarification about my use of the term brain death:
I use the term brain death in the more general sense to mean death of the brain independent of the rest of the organism. The question being asked here is, if you had a body in front of you with, for example, a cervical spinal cord injury effectively severing the head from anything below it, but the body kept on ECMO to maintain oxygenation, how could you tell a living brain from a dead brain? How could you differentiate a patient who, given massive resources, has a chance, from one who has none? This especially applies in cases of coma or similar