Well, perhaps Katara is kidnapped by a bounty hunter who has been hired by someone who has a vendetta against the Avatar's team. The kidnapper could be taking her to a far - off and desolate location. Then, Aang and the others have to track her down through various difficult terrains. Or, it could be that she's kidnapped by a group of dark benders who want to study her waterbending to find a way to corrupt it. They might keep her in an underground lair filled with all sorts of dark magic - like contraptions.
One idea could be that their kids discover a new bending technique that combines air and water bending in a unique way. For example, they create a sort of ice - air blast that can freeze and shatter objects simultaneously. Another plot could involve the kids going on a journey to learn about their parents' past adventures and in the process, they face challenges that test their own bending skills and teamwork. They might encounter an ancient spirit that only responds to a combination of air and water bending, and they have to figure out how to work together to communicate with it.
Maybe a plot where Aang and Katara's family gets involved in a diplomatic mission to the Fire Nation. Their children are exposed to a different culture and way of life. Along the way, there are some misunderstandings and cultural clashes, but in the end, they manage to strengthen the relations between the nations. And during this time, the family also discovers a hidden secret about the Fire Nation's past that could change everything.
Maybe Katara gets transported to Camp Half - Blood. She initially struggles to fit in but then she realizes she can use her water - bending skills in new ways with the help of Percy's understanding of water - related powers. They could then go on a quest together to find a way to send Katara back home, all while forming a strong friendship and learning from each other's cultures.
One interesting plot twist could be that the kidnappers turn out to be working for an old enemy of Zuko's family. They initially thought it was just a random act of villainy, but as the story unfolds, they discover a deeper conspiracy aimed at destabilizing the Fire Nation. Another twist might be that Katara discovers she has a hidden power that she can use to help them escape, but using it comes with a great cost. Maybe it drains her life force or has some other negative consequence.
Another plot could be that Rapunzel is kidnapped by a mysterious figure from her past that she doesn't remember. As she's held captive, she starts to have flashbacks of her early childhood and discovers secrets about her family. Meanwhile, Flynn Rider and the others are on a frantic search for her, and Rapunzel has to find a way to signal them while also dealing with the revelations about her past.
One idea could be that a rare and powerful Pokemon is kidnapped by a mysterious organization aiming to use its power for evil. A young trainer then sets out on a dangerous journey to rescue it. Another could be a Pokemon being kidnapped from a Pokemon sanctuary, and the local Pokemon community unites to get it back.
Maybe Mirajane is kidnapped by a dark wizard who has a vendetta against her family. In the fanfiction, the wizard could be trying to force Mirajane to reveal the secrets of her family's magic. Her Fairy Tail comrades would have to figure out where she is and how to defeat this powerful foe.
Well, a plot could involve Spock kidnapping someone to protect them from a greater danger that he knows about but others don't. For instance, he kidnaps a young, talented cadet who has a special power that an enemy race wants to exploit. He takes the cadet to a hidden location on a Vulcan outpost to keep them safe until he can figure out how to deal with the approaching threat. Or perhaps he kidnaps a diplomat who is unknowingly carrying a virus that could wipe out Vulcan, and he needs to keep the diplomat isolated until a cure can be found.
Maybe the witches kidnapped the character because they believe the character is the key to a prophecy. The character could then try to find out more about this prophecy and use it to their advantage, like befriending some of the nicer witches to help them escape. This could involve a lot of exploration within the witches' lair, finding hidden passages and ancient scrolls that hold the secrets of the prophecy.
One idea could be that Serena is kidnapped by a mysterious group who wants to use her unique abilities (if she has any in the fanfic's universe) for their own gain. For example, if she's a great athlete, they might want to force her to compete for them illegally. Another plot could involve a jealous rival who kidnaps Serena to stop her from achieving a great success, like winning a big tournament. Or perhaps Serena is kidnapped by someone who mistakes her for someone else and the whole story is about her trying to convince them of their mistake while also trying to escape.