If you're unaware, and you might not be, until very recently, an owner of a collection could hide the works in it with a single click of the button, without author's consent, essentially making the work disappear for everyone but the owner of the collection. This has changed but I am still wary.
I only add my works to collections I myself or my friends moderate.
If you want to save a fic in a collection—worry not, there's a way that doesn't damage anyone! Save a bookmark on the fic and then add that bookmark to the collection. This method doesn't allow you any power over the work so you can't accidentally mess up anything, and the bonus point is that the author doesn't have to manually accept the request for the bookmark to appear in the collection because it's yours!