It could be a new villain who has heard about Tails' mechanical skills. This new baddie might think that by kidnapping Tails, they can force him to build powerful weapons for them.
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.
As mentioned before, Eggman is a likely candidate. He's always had his eyes on Tails' skills and would stop at nothing to use them for his evil plans. So he could be the one behind the kidnapping.
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 possible plot could be that Tails is kidnapped by an old enemy seeking revenge. Maybe Eggman wants to use Tails' intelligence for his own evil schemes. He could hold Tails captive in his secret lair and try to force him to build some powerful weapon.
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.
Often, there could be a theme of adjustment. Tails having to adjust to his new, larger body. This could involve things like how he moves around, his confidence levels, and how he interacts with the world around him. It might also touch on themes of body image, as he might struggle with how he looks now that he's fat. There could also be a sense of adventure where he has to overcome new challenges because of his size, like fitting through small spaces or being slower in movement.