Obviously, Dumbledore himself is the central figure. Then there would be characters like Harry Potter, who might have mixed feelings about Dumbledore after learning some of his secrets. Hermione Granger could also be involved, using her logical mind to analyze the situation. And perhaps members of the wizarding government, such as the Ministry of Magic officials who might be the ones to judge Dumbledore.
One possible plotline could be Dumbledore being judged for his actions regarding Harry Potter. For example, some fans might write about how his decisions to keep certain secrets from Harry were either right or wrong. Another could be his past associations being put under the microscope, like his relationship with Grindelwald.
There's also a chance that Dumbledore gets caught by a group of rogue magical creatures. For instance, if he was exploring an area that was supposed to be off - limits to wizards and the creatures there saw him as an intruder. They might not be as rational as wizards and could hold him captive without really understanding who he is.
There may be such extremely non - canon and inappropriate fanfiction out there in the vastness of the internet, but it goes against the original nature and values of the Harry Potter series. J.K. Rowling's world has certain boundaries and this concept is far from what was intended in the original story.
It could be Severus Snape. He has a complex relationship with Dumbledore. Maybe Snape discovers some of Dumbledore's plans that he doesn't agree with regarding Harry Potter. He then sends a Howler in a fit of anger to express his disapproval.
Fred and George Weasley are very likely candidates. They are known for their love of pranks and their mischievous nature. They might see pranking Dumbledore as the ultimate challenge.
The Ministry of Magic could be responsible. They might be jealous of Dumbledore's power and popularity. They could see him as a threat to their own authority and come up with some false charges to arrest him. For example, they could claim he was hiding information about a dangerous dark wizard.
In the fanfiction, the Howler could be a warning from an unknown dark force. Dumbledore has been making moves to counter the rising dark magic in the wizarding world. This dark force, not wanting to be thwarted, sends a Howler as a form of intimidation. The Howler could contain veiled threats and references to past events that only Dumbledore would understand.
In some fanfictions, Dumbledore is portrayed as having a lot of secrets. If he gets caught, it could be related to his past. Maybe some old enemies find out where he is and catch him. Then he would have to deal with his past coming back to haunt him. His friends might try to rescue him, but it would be a very difficult situation for him, and it could change the whole dynamic of the fanfiction story.
One possibility is that Dumbledore gets caught spying on a group of Death Eaters. This would put him in a very dangerous situation as the Death Eaters are extremely cruel and loyal to Voldemort. He might be tortured for information about the Order of the Phoenix. However, Dumbledore is very resourceful and would probably be able to hold his own against them for a while, giving his allies time to figure out a rescue plan.