When a person's neck is broken, their behavior is altered, and we can say that some of the functions below the neck remain; these are due to the somewhat autonomous nature of the spinal cord. We cannot tell what has happened to the behaviors that are not exhibited anymore. The information needed to exhibit them might be disposed of, stored, or still dispensed and blocked along the way to its receiving point.
I am wondering about the effects of a similar separation of the nervous system at a point higher up than the neck. We have used the cut spinal cord quite often as an example of how each of the five sections of the nervous system acts on its own to an extent, but how representative really is that example? I can imagine many more complications we would have to account for if a cut was made, perhaps, between the diencephalon and telencephalon. Would this person be deprived of smelling since the olefactory nerve is on the telencephalon and the part of the brain that is most crucial to regulating body activity is the medulla (which contains the vagus to control the heart and other organs)? Would this person be deprived of thinking or of consciousness that they were thinking, since the neocortex is such a large area of input processing? Would this person be able to think and smell and do nothing else? Would this person be dead? (Where does the "person" exist?) Certainly the bundles of axons such as the spinothalamic fibers that ascend all the way to the neocortex would be interrupted. I am inclined to think that a cut at this location would result in an array of partial behaviors and complete chaos in the nervous system without the direction of the telencephalon and neocortex, rather than the simpler scenario of the two divisions continuing to function without communication as in the model we work with in class. It strikes me that there is some organization to the cranial nerves, with the less crucial nerves toward the front, but I do not think this implies that there are less crucial parts of the brain. All of the brain's wires appear so tangled and interconnected at this point that any disturbance could cause the entire system to crash.
Very nice extension of questions discussed in class to a new, entirely appropriate, and fascinating set of issues. In general, the spinal cord example is quite representative: the various "boxes" of the nervous system really ARE SEMI-autonomous (they go on working, though somewhat differently, in isolation), and we'll see this over and over again, including in cases which approximate what you've described (isolation of forebrain structures, to varying degrees, from more caudal structures). Classic experiments on the frog show some, but not a lot of difference in behavior when the forebrain is separated from the rest of the nervous system (I'm actually thinking about redoing some of those in light of some other work, want to help?). No, they're not dead (nor do they crash). Humans? I can make some guesses (the situation is different because of the neocortex) but don't know of clear clinical material that would answer your questions. It may exist though, and it would be worth looking at clinical publications to see how good a guess one can make. PG