Brain Death

clinical death, situation in which one's brain is not functioning and a person cannot live without life support

Brain death is a legal definition of death that emerged in the 1960's as a response to the ability to resuscitate individuals and mechanically keep the heart and lungs working. In simple terms, brain death is the irreversible end of all brain activity. It should not be confused with a persistent vegetative state.
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Brain death n. Irreversible brain damage and loss of brain function, as evidenced by cessation of breathing and other vital reflexes, [more]Brain death - Community and Resources

Noun
1. death when respiration and other reflexes are absent; consciousness is gone; organs can be removed for transplantation before the heartbeat stops
(synonym) cerebral death
(hypernym) death