Perhaps I'm just an anal control-freak, but I'm always the one to fill-out, maintain and keep all of my players' character sheets between sessions. No one at my table seems to mind since they seem to like my clean and clear penmanship. They're free to fill out and keep their own copy if they want one for themselves, but so far nobody's bothered to. I started keeping the players' sheets in my DM binder years ago after I got tired of people forgetting to bring them to the game and being forced to scribble out a makeshift copy based on their vague recollections during the game. I also hated being unable to read some of their messy sheets and finding errors.
This way we're certain that no one is lacking for their sheet, it's always up to date with their current xp (which I add in between sessions) and stats. If the player can't make it, at least we still have his character sheet so that the PC can continue adventuring with another player or I running it. When they level-up, I make the appropriate changes and email the players to ask them about new spells, feats or skill that they need to choose. Hit points are rolled and added to the sheet when they show up. This has even spread to other groups I'm in, with my fellow players asking me to fill out their sheets when they level-up. I enjoy doing it so why not?