Usually, we just treat the character as there, but not usefull. He just kind of vanishes and appears again at the next session. The only exception is when there is something that only that character can do, and even then, its used sparringly.

Another DM I played with used the characters as NPC and played them to the best of his ability, trying to do what the player would do. Nonetheless, he made it clear that he wouldn't kill that pc, except in a TPK, because that would be "unsporting".