Hello, I'm an expert in neuroscience and medical physiology. Let's dive into the question of whether someone can be brain dead and still breathe on their own. Brain death is a legal and clinical declaration that an individual has sustained either irreversible cessation of all functions of the entire brain, including the brainstem, or irreversible cessation of circulatory and respiratory function that can be expected as a result of either irreversible cessation of all functions of the entire brain or of the brainstem. The brainstem is the part of the brain that controls many of the body's most vital functions, including breathing, heart rate, and the sleep-wake cycle. When a person is declared brain dead, all brain functions, including those of the brainstem, have ceased. This means that the person is no longer breathing on their own. Instead, mechanical ventilation is used to maintain artificial respiration. The body may still show some autonomic functions, such as a heartbeat, due to the action of the nervous system and the release of certain hormones, but without brain function, these functions are not sustained and will eventually cease. read more >>

When the breathing machine is turned off, a patient who is brain dead will not breathe. The heart will beat for some time after the brain dies as long as breathing is artificially maintained because heart function is not entirely dependant on the brain.read more >>