The brain completely controls the bodies functions. When people are brain dead we can keep them alive with machines, but only physically alive and they are in a vegetable state. Tom i’m sure can tell us more.
Parts of the brainstem are required for the control of basic bodily functions such as breathing, but it is possible to “survive” if large parts of the thinking brain are destroyed or damaged beyond repair. But life without thought, memory, movement, sensation, communication, and with no chance of recovery would in my view be meaningless – not so much life as existence, and a very unpleasant one for loved ones to endure. This is called a persistent vegetative state (PVS). However great care has to be taken with the diagnosis, as there are cases of people recovering brain function. Recently Adrian Owen and colleagues used brain imaging to determine that patients in an apparently vegetative state were conscious by asking them to imagine different activities (playing tennis, walking through a house) to indicate yes or no. In an fMRI scanner the patterns of activity produced by these imagined activities are quite different. A few of the patients were able to answer yes/no questions in this way.