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.
It could be a rogue Saiyan who wants to take over the Saiyan throne and thinks kidnapping Goku is the first step.
In a 'l gets kidnapped fanfiction', there could be a lot of drama. Maybe his friends would start a search mission right away. They might follow some small clues like a piece of cloth from his clothes left at the scene.
Well, his friends might launch a rescue mission. They would use their various skills to track down where Kakashi is being held. Naruto could use his shadow clones to search different areas, while Sasuke might use his Sharingan to detect any hidden threats on the way to the rescue.
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.
If Sakura gets kidnapped by the Akatsuki in fanfiction, Sasuke could also get involved. Since he has his own history with the Akatsuki, he might use his knowledge to track them down. Also, Sakura herself could be trying to find a way to escape from within. She's a strong kunoichi, after all. She might be gathering information about the Akatsuki's plans while being held captive.
Another scenario could be that the kidnappers have some sort of ulterior motive related to Sora's special powers. They might try to extract that power from him, but Sora, being the strong - willed character he is, would fight back in some way, even while being held captive.