Cells need two things to survive: oxygen and glucose. Without each of these, brain cells begin to die. If oxygen and glucose are removed completely, the damage continues and the brainstem dies.
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The reason any human is living is because they breathe in oxygen, which is transported to cells by blood. All human cells need oxygen to go through cell respiration and produce energy for the body. Without breathing, and subsequently oxygen, the first cells to die will be in the brain, causing death for prolonged periods of time.
The same goes for blood; if there's no blood flowing, there's no way for the oxygen to be transported from the lungs to the various cells.