Readers write stories set within the world an author created. They are called fanfiction. They use characters from their favorite author to write their own story. Sometimes they create their own character to roam the world. The fandom of fanfiction is complex. Some fics are great while other can be terrible, but they all share the same love for the writer's original work.
Fans always think of the 'what ifs' and start to write them out. One of my favorite 'what if' scenario is Harry Potter and Hermione Granger as a couple. I love to read them and check every few weeks for any new stories. 'What ifs' enter the realm of that isn't possible based on canon (original timeline) material. Another couple pairing from Harry Potter is Draco Malfoy and Ginny Weasley. Based on the Rowling's novels, there is no way those two would ever happen. But the fans thought of the possibility and went for it.
The pairings and scenarios written by fans are vast. Each fandom shares the terminology or scenario but some are unique. For example, a fan labeled as 'fluff' generally is happy content fic with little to no plot. They aren't long pieces and cover the little things in life. The best known scenario in anime fanfiction is the 'blanket scenario'. Basically, there is one blanket for two people to share during a cold night. They range from explicit to fluff material.
The best resource to read these works is Fanfiction.net. The website has been around for over 10 years and is the first centralized location for fans to share and comment on fics. The site sorts fandoms based on whether it is a book, TV show, movie, etc. Some fans write stories with more than one fandom together called 'crossovers'. For more lingo, visit this link.
Challenge: Check out the Fanfiction.net and read your favorite book or TV show fics by other fans and report back on your experience.