There's also a possibility that it's a misanthropic Pokémon that just doesn't like humans interfering in the Pokémon world. It sees Ash as a symbol of human intrusion and decides to kidnap him with the help of the eevee to send a message to all human trainers.
Well, perhaps Pikachu would go on a heroic quest to rescue Ash. It might team up with other Pokémon like Charizard. They could follow the kidnappers' trail, facing various challenges along the way, like battling wild Pokémon or getting through difficult terrains.
A new villainous trainer group. They might see Ash as a threat to their plans of dominating the Pokémon world, so they kidnap him to stop him from competing in important battles or tournaments.
It could be an enemy from one of his past cases. Someone who holds a grudge against L for getting them caught or ruining their plans before.
It could be a rival guild member who wants to use Juvia as leverage against Fairy Tail. Maybe someone jealous of her powers or her relationship with Gray.
The Death Eaters are an obvious choice. They've always been after Harry, so they could easily be the ones to kidnap him. They'd want to take him to Voldemort to prove their loyalty and also to finally get rid of Harry for good.
In some 'damian gets kidnapped fanfiction', the kidnapper could be an otherworldly being. Let's say an alien or a magical creature that has an interest in Damian for some strange reason. It could be that Damian has a unique energy or power that the otherworldly being wants to study or harness. Or perhaps it's a human who has been corrupted by some dark magic or technology and is acting on behalf of a more powerful, hidden force that wants Damian for its own nefarious purposes.
Maybe it's a group of poachers who are after rare Pokémon. Gengar, being a relatively unique and powerful ghost - type, would be a valuable catch for them. They could plan to sell Gengar on the black market for a high price.
In a fanfiction where Ash is reincarnated as an Eevee, his journey would be very different. Firstly, his physical abilities would be limited to what an Eevee can do. He couldn't just run around freely like a human. However, his knowledge of Pokémon battles and the world in general would be a huge advantage. He could potentially form alliances with other Pokémon that he knew were strong from his past life. Also, his relationship with Pikachu would be interesting. Would Pikachu recognize him? And how would Ash, as an Eevee, interact with Pikachu now?
The Death Eaters are a likely choice. Since Snape was a double agent, some of them might have suspected his true loyalties all along. Once they got the chance, they would kidnap him to either punish him or to get information out of him about the Order of the Phoenix.
It could be Shredder. He's always been after the turtles.