I've been reading a number of books on the issue:

Life After Life by Dr. Raymond A Moody,
Near Death Experiences - the rest of the story by PMH A****er,
Journey of Souls by Michael Newton, Ph.D., and yet to read,
Science and the Near Death Experience by Chris Carter.

From these various sources, as well as clues picked up by reading Robert Monroe's books, and what Mellen-Thomas has to say about his own near death experience, I am inclined to think that when the body-machine stops, the soul leaves. There is no point for it to stay. And then of course there are those cases where the doctors manage to reactivate the physical and the soul is drawn back in and it's out of those that we've been fortunate enough to learn just a bit about what may be expected when we make the transition individually.