I think about that often. In fact at one point I considered writing a book in which a selection of characters from some of my favorite novels (written by other authors) live in a high rise apartment house called Century Towers. These characters begin to fade over time and when the day comes when no one reads their books they vanish completely; their apartments left silent and empty.
As for my own characters, I don’t wonder at all about them after I’ve completed the book. Funny, isn’t it?