Depends on the Player
Not everyone is okay with playing a character who's not entirely theirs, or having a character of theirs played. However you do this, there are really two possible options:
- The character is yours, a NPC, and is treated as such.
- The character is theirs, a PC, and is treated as such.
This will inform your course of action as events unfold:
While it is conceivably possible to just leave said character out of play entirely when the player is gone, this has its own disadvantages, namely always changing up game balance, which could be an issue if you write content ahead of time and the action advances at an unforeseen pace.
If it's an NPC
You control it outside of sessions, you advance them, and generally manage them. This is great for players who are versatile and enjoy roleplaying characters they normally wouldn't build. The player who joins only borrows the character, and it's otherwise managed by you. This approach works well when:
- The player is flexible or less invested in the campaign (or just doesn't have time)
- You and the player can communicate frequently
- You and the player have similar goals and expectations in writing
- The player is fine giving you final control of the character
This has a few advantages:
- If the character is clearly a NPC, you have the final say in disputes
- Having the character die is significantly less likely to backfire
- You manage the character, always keeping it on hand and making it available for the group
Note that it's perfectly acceptable to hybridize the roles here; you may ask the player what they'd like to see the NPC get as they level up, but you're doing the story writing and characterization for the character. Alternatively, you could pass control of the NPC around between sessions, and just manage how they level up and their roleplaying traits.
If it's a PC
They control it outside of sessions, advancing them, etc. You or other players control the character while the player is absent, but generally the character is treated like any other character whose player is absent. This approach works well when:
- You don't have time to manage another NPC
- The player wants to stick to his vision of a character
- You and the player have different goals
- The player wants to maintain a certain degree of control
This has a few advantages:
- The player is more likely to be engaged in the game
- The character matches what the player(s) want them to be
- The player is responsible for keeping the character ready
Again, the logistics of who controls the PC between sessions are negotiable; the controller should be chosen by the player. Using a committee is possible, and may produce better results in some cases, but requires more cooperation.
Some parting notes
When dealing with a character like this, it's not necessary to follow the rules entirely. Here's how I'd handle it:
- Giving the character plot armor when the player is away
- The character advances like any other character (or at average speed, if advancement is based on things an absent player is unlikely to accomplish)
- Re-cap outside the game, so that the player knows what is going on, but doesn't slow down play