One of the basic tenets of Kabbalah (Which I don't profess to understand fully, but I do believe is correct in many of its ways of interpreting the world) is that there is an entire world around us that we are unable to perceive with the five senses. All kinds of actions, reactions and processes occur outside of our perception. As an extension of this our senses are growing, through science we are able to 'sense' all sorts of things from enzymatic reactions, DNA collation, even molecular and sub-molecular processes. I believe that right now, with current technology and human understanding the only possible honest answer is "I don't know" but I believe we will eventually extend our perception enough to figure out 'where' a personality is located within the brain, and what happens to it when biological function ceases.