What is it called when a person is in a state characterized by prolonged cessation of all brain activity and complete absence of voluntary movements?

This state is called brain death. It is a highly controversial issue in the medical field, and there is a lot of research around the subject. This is basically what happens when a person has died. Even if functions normally controlled by the brain can be sustained artificially (life support machines), doctors and other professionals all agree that when a person is in a state of brain death, they can accept to declare the person dead. When a brain has reached "brain death," the person cannot breathe by themselves (which is a spontaneous action - normally, you don't have to think about breathing in order to breathe), there would be no more brain waves, and the heart will have stopped beating. There would also be no response to touch, pain, noise or other types of stimuli. 

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