Where to begin... This was the single most frequent offense on the site before the Great Reconfiguration of Aught-Four. Many users completely ignored the stated point of this website, and instead treated it like "Hey! Free publishing! Time to collect me some fans!" So they went off and wrote their stories, which was good, and wrote "Please don't add on; I'll finish this later!" in the About The Author box, which wasn't so good.
I've seen this problem crop up especially around fan-fiction. One person wants to write her own story about Yu-Gi-Oh, and she gets mad when others' contributions are inaccurate to the characters as we know them from TV. Another wants to do a text adaptation of his favorite Pokemon episode, and he doesn't want someone who hasn't seen the episode to "mess it up".
Well, you know what? Too bad. You don't get to protect your story from others' influence. It isn't "your" story after all. All you can lay claim to are your chapters; the story itself belongs to everyone.
So if you start a story, you have to practice a certain amount of detachment. Think of it as as exercise in imagination and typing.
This site is not a publishing house. It does not host deathless masterpieces. This site is a game. The point is not the finished story (besides, the stories are by nature never finished, they're neverending, get it?). The game's about the unpredictable nature of interactive fiction.
Put it another way: Imagine, if you will, that I'm throwing a party. I've cleared off the couches, I've set up a punch bowl and some cheese-and-cracker trays, and I'm serving dinner. You don't get to tell your fellow guests, "Hey, get your hands off that punch, only I am allowed to drink the punch!"
I'm hosting this party, and I say everyone gets to drink the punch. I'm running this game, and I say you are all invited to play. And it would be a pretty piss-poor interactive fiction site if random schmucks attempted to mark certain stories as their territory and discourage random interaction therein, now, wouldn't it?
Thankfully, it's easier to delete a chapter than it is to clean up cat spay. I've done both. I should know.
The moral of this story is: If you can't stand the possibility of having other players add on to "your" story, foot the bill for publishing it yourself. Put it on your own website. But if you put it here, it's fair game.