Depends if it’s Fair Use or not.
Display and distribution of fan art that would be considered a derivative work would be unlawful. However, American copyright law allows for the production, display and distribution of derivative works if they fall under a fair use exemption, 17 U.S.C. § 107.
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You’re mixing up things a bit. Fair use says that under some circumstances, you can legally violate copyright when making something, even if the copyright holder complains. For example, quoting from a book in a review is violating copyright, but it’s normally considered fair use. Fair use is a complicated matter and unless there’s clear precedent, most of it is really decided by courts on a case-by-case basis.
Companies don’t “permit” fair use–if something is fair use, it doesn’t matter if the company has a problem with it or not. What you’re referring to here is something I don’t think there’s a technical term for, so I’ll call it the “don’t care exception.” Basically, if the copyright holder doesn’t care about you violating copyright, you’re effectively in the clear. A lot of times people will claim that video game playthroughs on YouTube are fair use, but that’s actually a questionable claim–especially given that a lot of them are monetized (something being done for profit makes it more difficult to qualify as fair use). But they fall under the “don’t care exception” because almost no companies have enough of a problem with it to actually take any kind of legal action against it (some encourage it!).