How do you cope with the absence of a player, either in a single session or repeated absences?
In one word: poorly.
Much as Ginger related, characters of missing players will often develop Etherealness, or just fade into the wallpaper. What’s done often depends on the size of the group and the style of game played.
For our current Dogs in the Vineyard game, the absence of any player is enough to kill the evening’s game. This is because there are only three players- one person’s absence means only two people are playing. We could soldier on (the system and conflicts would still work out fine; really, there’s no “challenge rating” to screw up), but would feel awkward excluding the absent person. Which is too bad; it means less gaming.
Larger groups (with 5+ players) demand that you’re able to play with someone absent- or you’ll never play at all. We’ve had a great deal of trouble with this though- particularly when people miss early sessions, when a team is still gelling. This was a significant component of the last Mage game’s collapse- Kev missed several weeks. When he returned, it was clear that another character had taken over his niche, thoroughly. It’s tough to pretend a character’s essential when the player’s absence shows that you can survive without them.
In more combat oriented games, it’s common for the group to play absent characters. This can be greatly annoying, since running a second (and unfamiliar) character really cuts into the time I’d rather use for characterization.
Penalizing absent characters can be tough too. (I have great doubts about doing so at all, and have argued against penalizing absent characters in D&D. Unbalanced character levels make things difficult… and can really threaten the role of a character who’s just a level or two behind, if the game is still at low levels.) I assume that players would rather play than do other stuff (not always a valid assumption)– either way, character incentives aren’t going to be enough to persuade most people. And I’m not gaming to judge my fellow players, so player incentives are definitely no go territory.
Games with multiple parallel plots/ story lines (instead of 1 team plot/ party play) work out best of all- the absent character just isn’t spotlighted. When the player shows up, he may explain what the PC was doing (if it’s important)– but during the session, it’s easy enough to proceed without them.