In the fanfiction, Ash's friends from the Pokémon journey, like Misty and Brock, would probably be really worried. They could start their own search. Maybe they'd ask for help from local Pokémon trainers or even some Pokémon professors. They'd use their knowledge of the surrounding areas and the habits of kidnappers to try and find Ash.
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.
It's possible that the eevee that's involved in the kidnapping has some ulterior motives. Maybe it was forced to do it by a more powerful and evil Pokémon. Ash, while kidnapped, could be trying to reason with the eevee, understanding its situation and trying to turn it into an ally against the real bad guys behind the kidnapping.
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.
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?
Well, he could be used as a bargaining chip. Team Flare might try to exchange Ash for some powerful Pokémon or valuable items. They could also try to force Ash to reveal any secrets he has about powerful Pokémon or rare items he's come across during his travels.
In such a fanfiction, Goku might be kidnapped by a powerful new villain. His friends would then start a search mission. Maybe Vegeta would be the first to volunteer, thinking it's his chance to prove he's stronger than Goku.
In the 'ichigo gets kidnapped fanfiction', he might be rescued by his friends. For example, his comrades from the Soul Society could sense his distress and come to his aid.
In the 'darkrai gets kidnapped fanfiction', perhaps a group of trainers who want to control the power of the Legendary Pokémon Darkrai kidnapped it. They might be planning to force Darkrai to battle other Legendaries. This would create a lot of chaos in the Pokémon world as Darkrai is a very powerful and mysterious Pokémon.
In such a fanfiction, perhaps there would be a heroic rescue attempt by her family. They would use their unique powers to track her down.
In such a fanfiction, Tails might be kidnapped by an old enemy like Dr. Eggman. His friends, like Sonic, would then start a rescue mission. They would search all over the place, from the Green Hill Zone to Eggman's secret bases.
Well, in the fanfiction, Gengar might be held captive by some powerful villains who want to use its powers for their own evil plans. Maybe they'll try to force Gengar to haunt a particular place or to attack someone. The Pokémon trainers in the story could then start a rescue mission to save Gengar.
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.