fanfiction

What makes people write them? Same reason why doujinshi mangas exist, fans just want more and if the authors don't give it to them then they just got to do it themselves. I don't write fanfics (not one of specialties) but I have done a few Zelda doujinshi mangas back in high school when I was full of questions like who Sheik really was and who the fierce diety masked person was in Majora's Mask before I was able to beat both games. I didn't have easy access to the internet at the time so I decided to make up my own answers by making up my own Zelda comics.
Even after finishing the games, some people may not have liked with the way things ended(like with character coupling) and create fanfics, modifying the story to their satisfaction. There's also cross-over fanfics where fans completely change the story by introducing characters to others from a different show/game/movie just to see how it'd be like. I honestly don't like those types of fanfics, though.