In my games, if the player gets a copy of the character sheet to me, another player runs the PC for the game. They usually don't take much part in roleplaying, and are played very cautiously in combat. They CAN die, but it's generally understood that great effort will be put into them NOT dying. There is also care exercised in using up their disposable resources (like potions). They get half XP for the session.
If I DON'T get the character sheet, the PC isn't there, no matter how odd it is for them to disappear at the time. They go back to chill with the horses, wander away, got caught up doing something and will catch up with the party later, whatever. No XP.
In one campaign, I anticipated having people go missing spontaneously fairly often, and I didn't feel like dealing with the hassle of pawning character sheets off onto other people. So when folks were missing, their characters were suddenly teleported into a small room that was completely silent and dark. Light sources didn't work, and there was no way out. I tied the room into the plot for the end of the game.
I like the stone idea.