In Japan, self-published works are called doujin works. Many of them are derivative of existing works, like commercially published manga and anime. What's special about them is that they are openly sold. Comiket, the most popular event for buying and selling doujin works, has over 30,000 individuals and groups selling stuff, and over 500,000 total attendees. Twice a year. Not everything there is based on existing works, but a lot of it is.
It's not technically legal to sell these derivative doujin works, but it's still allowed by the vast majority of copyright owners because the derivative works 1) don't duplicate or compete with the original, 2) help to create a fandom that draws in more people and sustains interest in the original work, and 3) train new talent who will go on to publish their own commercial works. The doujin scene is important enough that the prime minister recently announced that derivative works will continue to be allowed even if the TPP becomes law (or in other words, it will still be left up to the copyright owners to decide if they want to allow them or not).
A particular success story in the doujin scene has been the Touhou game series, which has been authored and self-published by just one developer since the 90s. The series wouldn't have even a fraction of its huge popularity without the massive amount of derivative works based on it (manga, art, fanfiction, games, anime, music). There's now loads of commercially produced Touhou merchandise, and several manga series, and the series could be commercially even bigger if the author wanted it to be. But it would never have gotten this far without the doujin scene, and might not even exist in the first place without it.