No they don't..you get rid of characters if it fits your story, not because there's some law that says you have to do it. If it serves your story OR if there's some behind the scenes drama going on that can't be resolved, then you kill them. But killing people just for the hell of killing people is lazy, slack ass storytelling and bad writing.
When a character dies on the walking dead, it often does something to other characters, propelling them in one direction or another and its in service of those characters.
The West Wing is one of the greatest shows ever and the only time major characters died is because one actually died in real life and the other made a joke about leaving the show so she was written out but in both cases, it was in service of the show and the story. Whenever you're writing something the first thing you need to ask yourself is "what's the point?" If there's no point, then keep them alive.