They would lose any magical powers they may have had in the book, but anything they are, rather than can do, will stay. For example people from the His Dark Materials world would keep their daemons. You can take them out at any time in the story’s plot, but for all other people consuming the media, it will be shown that the character suddenly disappears, with the rest of the plot being affected accordingly. People will notice this happening. The character is not under any sort of control by you once you have taken them out of the story, although they will appear next to you to start with.
Oof in that same vein, we could use a Samuel Vimes sort wandering around dispensing justice…
I was thinking Vimes, but I’m not sure I could handle the guilt of taking him from young Sam.