I run short-term campaigns in a long-term setting.
Characters do -NOT- fade into the background once they are out of the story arc. They remain part of the game world, and I do with them as I will, as long as it feels consistent for the character -and- the setting. The campaign is twice as memorable if the players can encounter, hear about, work against or work with the characters from their prior story arcs.
Then again, it is accepted that the players will quite likely NEVER get a chance to play the old characters again once a new game has started, and that *I* am the owner of the campaign setting, mutable as it may be.
Only one player ever complained about this, and he no longer games with us. Effectively, if you don't want your character reappearing in my campaign setting, make sure he's REALLY dead before the campaign ends.
Or don't play.