This is a fascinating question, and it's the kind of thing you might come across in an exam in a copyright law class. I hold a J.D. but am not a lawyer, so this is not legal advice. I'm just running through a few questions that spring to mind.
Is What's on the Character Sheet Protectable by Copyright?
Perhaps it's the sum of everything on the character sheet. But the character sheet itself was likely created by the game's publisher, so the publisher would own copyright on the sheet.
That copyright extends to how the character is defined. For example, a D&D character is defined by Strength, Constitution, and other specific attributes. And while my Cleric Clive might have STR 15, CON 14, WIS 17, INT 12, DEX 10, and CHA 12, so might other Clerics. The spells that character can cast are defined by Wizards of the Coast. The term "Fireball" is not owned by WotC, but when used on a character sheet designed and published by WotC for use with Dungeons & Dragons, the word clearly refers to the spell of the same name. The expression of that spell's effects are published in the Players Handbook and are owned by WotC.
The content on the sheet that could most clearly be considered the work of the player would be any notes regarding backstory, appearance, behavior, personality, and so on. So the specific words used to describe the character could be protected by copyright. This would extend to characteristics such as Aspects in Fate Core, which are defined by words from as well as numbers.
Copyright for a character is tricky even when it doesn't stem from a game system with predefined characteristics. In order to get copyright protection for a character, distinct from the work in which it appears, you have to prove that the character is unique and distinctive enough. In other words, absent distinctive backstory and characteristics, a D&D Cleric with a standard mix of spells and characteristics within the normal range for Clerics might not warrant copyright protection. Clive might or might not be distinctive enough. Because tabletop RPG characters are necessary each tied to a game system, they are bound to the game system. Proving that a character created in such a way could by protected by copyright seems like a stretch, because so much of what makes that character is actually a product of the game itself.
Is Using the Character in a Game a Performance?
Performance of a work can be covered by copyright. If I write a story featuring my Clive the Cleric, I automatically hold the rights to performance of that story. So you couldn't record yourself reading my story, then distribute that recording, without running afoul of my copyright on the work.
But a character sheet is not a story. It's akin to the notes an author makes about a character when writing a story, but it is not the story itself. So it's unlikely that using a character sheet during a game could be considered a performance.
Is Copyright the Tool for the Job?
As a practical matter, copyright is not useful in the abstract. It has to be enforced. Let's say for the sake of argument that Clive the Cleric is really unique and can be protected under copyright as a character. You take my Clive the Cleric character sheet and start using him as an NPC in your campaign.
I can tell you, "Hah! Clive is protected by copyright!" To which you could very well reply, "Sosumi!" Then I'd have to decide whether it was worth it to hire a $300/hr. attorney to put together a case. Assuming I shelled out a few thousand dollars to sue you, you could reply with a Fair Use defense, arguing that your use of my character was transformative and noncommercial; the character sheet itself was created for use in a game rather than for broader distribution; and while the amount of the work used was substantial, the effect on me was negligible. I could still keep using my character sheet, I could sell it to others or give it away, and it's highly unlikely that your use of the sheet would in any way affect me financially. Maybe you'd win the case, maybe I would. But we'd both be out a lot of money regardless.
Whatever is going on between you and I around Clive and whether his character sheet should be used in your campaign, we'd probably be better off finding another way of resolving the issue.
What's the Real Issue?
Maybe it's this:
If the character is then used in a different game can the player disregard something they did not give permission for happening to their character in the first game?
That's between the player and the DM to resolve, but it's a player character, meaning it was created and used by a player. Any time I've ever used a player character as an NPC in a campaign I was running, it was with the agreement of the player, and with the explicit understanding that the character would not suffer any permanent negative effects.
If the DM is having a hard time planning sessions where a player is unavailable and can't run their character, there are several solutions to that problem. The most obvious and easiest in my experience is that the character is simply away. Maybe he had to go tend to his ailing Uncle Zeb. Maybe he wandered off down a side passageway. Maybe he got really bad diarrhea and sat in the back of the wagon during the entire journey to the Dark Woods.