In many fanfictions where Gil gets kidnapped, it could be for various reasons. Maybe it's by a rival group who wants to use him as a bargaining chip against his friends. For example, in some stories, Uma's crew might be targeted because they are seen as a threat in the Isle of the Lost. Gil, being a part of that crew, gets kidnapped. Writers often use this plot device to create drama and show the loyalty and courage of the other characters as they try to rescue him.
One idea could be that Sam is kidnapped by a group of rogue hunters who think he's gone too far in his use of demon powers. They lock him in an abandoned bunker and try to 'exorcise' the 'demon' out of him, not realizing he's in control. His brother Dean has to race against time to find him, following a series of cryptic clues left by the kidnappers.
Natsu was walking through the forest one day when suddenly a group of dark mages emerged from the shadows. They quickly overpowered him with some sort of magic -binding spell. They dragged him away to an old, creepy lair. His friends back at the guild soon realized he was missing and set out on a search mission. Happy flew around frantically looking for any sign of his friend. Lucy, Gray and Erza teamed up and followed some leads they found in the forest. They were determined to rescue Natsu no matter what it took.
Peter's kidnapping was a carefully planned event. The kidnappers had been observing him for weeks. One day, as he entered a park, they grabbed him. They blindfolded him and took him to a secluded location. Peter was scared but he didn't show it. He started to befriend one of the kidnappers, a young guy who seemed a bit hesitant about the whole thing. Peter told him stories about his life and gradually the kidnapper started to have second thoughts. Eventually, the kidnapper helped Peter escape by distracting the others.
It could be a new character created specifically for the fanfiction. Maybe a young scientist who is working on a project related to the super - soldier serum. Since Bucky has a history with the serum, this would create an interesting dynamic.
A Gru bedtime story could be a story that features Gru, perhaps from the 'Despicable Me' franchise. It might be about his adventures before he became a father figure, like his early days as a super - villain planning his evil schemes. It could also include his minions and their zany antics that would make for an interesting and entertaining bedtime story for kids.
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, in a 'pit gets kidnapped' fanfiction, the plot could involve the search for Pit. Maybe his friends like Palutena start a quest to find him. They might face various obstacles and enemies along the way.
Perhaps it's an organization that wants to use Kakashi for their own evil plans. They might think that Kakashi's skills and knowledge would be useful for them. For example, they could be trying to create some sort of super - weapon and they need Kakashi's expertise in ninjutsu.