In the movie Cypher gets shot with an energy beam and his dead body is never seen. The movie never explores this, but it does leave the plot open for Cypher to escape and re-enter the matrix.
Here at the Cypher's Matrix Blog, we will explore life through the base concepts from "The Matrix" movie philosophy. i.e. we will look at events through the dynamic of reality being a defined 'matrix' that lays on top of a separate, but more actual reality.