What happened to the Cheshire Cat?

Answer 1

The Cheshire Cat first appears in Chapter 6 of Lewis Carroll's book, Alice's Adventures in Wonderland. During his conversation with Alice he says he'll see her at the Queen's croquet game later. When he arrives at the game, only his head appears and the King of Hearts takes an instant dislike to him. The Queen of Hearts orders that he should have his head cut off, but an argument ensues:

The executioner's argument was, that you couldn't cut off a head unless there was a body to cut it off from: that he had never had to do such a thing before, and he wasn't going to begin at HIS time of life.

The King's argument was, that anything that had a head could be beheaded, and that you weren't to talk nonsense.

The Queen's argument was, that if something wasn't done about it in less than no time she'd have everybody executed, all round. (It was this last remark that had made the whole party look so grave and anxious.)
The disputants all appeal to Alice, who tells them that the cat belongs to the Duchess, so the executioner goes to fetch her, but:
The Cat's head began fading away the moment he was gone, and, by the time he had come back with the Duchess, it had entirely disappeared; so the King and the executioner ran wildly up and down looking for it, while the rest of the party went back to the game.

Answer 2

The Cheshire Cat fades away leaving only its smile behind in Lewis Carroll's "Alice's Adventures in Wonderland." This is part of the cat's mysterious and whimsical nature in the story.