One thing about Tron that is important is that it is a metaphor for a computer system and not an exact duplicate of a computer system. Thus when things happen to the computer system what happens in the Tron world is a metaphor for what happens in the physical world.
The world of Tron in the first film appears to be one that matches the company network, so it appears to be a living and ongoing world which we can assume still exists at the time of the second film, although much changed.
However the world inside Flynn's 'server' in the second movie exists without external connection, that being one of the main points of the film. As it is pointedly 'saved' and shutdown at the end of the film, we have to assume that something like one of the following options occurs:
As the system is shut down the world starts to 'freeze' into stasis. Depending on point of view this could be horrifying for the programs, like dying, or perfectly natural, like going to sleep.
Alternately we can view this as the Tron world being 'sealed' so that while time appears to continue to pass (at one rate or another) within the world nothing can enter or leave. This would imply that somehow the world of Tron is not based on the digital bits that we use in real computers but at a lower level of atomic or quantum state.
Finally, excuse the pun, shutting down the system could be viewed as the world being utterly destroyed. This is how real computers work, the memory is copied to disk and then as the power goes it is permanently erased, only to be created from new when or if system is restarted. A horrifyingly final end.
As this is, above all, a Disney movie we can further assume that the creators did not intend for us to think that the world of Flynn's server and all it's inhabitants were cruelly destroyed. The scene where they are 'saved' implies a hope for the future, because, after all, I'm sure that Sam would want a chance to rescue his father.