Usually they don't . A fistula occurs when there is a serious infection, usually and abscess, between two internal organs or an internal organ and the skin overlying it. The infection destroys part of the tissues of both, and the body heals while leaving a hole connecting the two structures. Fistulas rarely close without intervention. Usually the connection needs to be removed so that the tissues can heal separately.
What kind of fistula. If you want a meaningful answer to this question you will need to say what type of fistula (where it is) and if you know what caused it. A fistula is a connection between two organs that should not exist. So there are too many types for anyone to answer this without more info.
Time or surgery. A fistula is basically an abnormal connection between two body parts. Depending on where the fistula is, sometimes it will resolve with time, but often these need to be treated with surgery.