I believe death is the cessation of life. When the body dies it is analogous to turning off a light switch or a computer. The current just stops. If we knew more about the brain it might be possible to examine the brain to see what experiences have made their way into the persons storage area. In my opinion the brain is much like the hard drive of a computer. Data is stored for long term use when needed. Consciousness is a function of the biochemical reactions and impulses generated by a living brain.
In so far as our lives touch others and we are remembered, we live on after death. In that sense our souls are immortal.