I've really tried to design adventures and campaigns so that they don't revolve around only one character. That way, if they die, there will be other sub-plots to run with.
I think if someone really threw an unwarranted hissy fit, I'd question whether they should be there in the first place.
True story from my early, early days of 1e DMing, 20 years ago(!):
Me: "You see a room with a bunch of blood and shredded rubble on the floor. There are two dead bodies in there, and both look like they've gone through the wringer. They still have all their gear, though."
Ken: "Cool! I go in!"
Me: "You sure?"
Ken: "Yeah!"
Me: "Okay, the ceiling sprouts spikes and falls on you. You're dead. It does like 40 something points of damage. Splat."
Ken: "I didn't go in there!"
Me (echoed by other players at the table): "What?"
Ken: "I didn't go in there! You misheard me!"
Me: "But you said...."
Ken: "No I didn't! I never went in there! I'm not dead; no you *can't* have my character sheet!"
Other player: "Dude, you suck. You're dead. Deal with it."
Ken: "No I'm not! I'm not!"
Ric: "Can I loot his corpse?"
He still denies it, too.
- Piratecat