Common themes in 'bakugou kidnapped' fanfiction often revolve around Bakugou's growth during the ordeal. He might learn more about himself or his relationships. There could also be a theme of mystery, where the identity of the kidnapper is slowly revealed through clues. And sometimes, the fanfiction will focus on how the situation affects the overall story - line or the world in which Bakugou exists, for example, how it impacts the hero - villain dynamic in the story.
Midoriya is often a common character. Since he has a complex relationship with Bakugou, his reaction to Bakugou's expulsion can be an important part of the story. All Might might also be included as he could be a mentor figure who tries to guide Bakugou, even after his expulsion. And Bakugou's other classmates like Kirishima would likely be there too, as they are his friends and would be affected by his leaving.
I'm not sure of specific 'bakugou kidnapped' fanfictions off - hand. But you can try searching on fanfiction websites like Archive of Our Own (AO3). Just type in 'bakugou kidnapped' in the search bar, and you should get a list of relevant fanfictions.
He might become more responsible. Since One for All is such a significant power, he'd have to step up. He couldn't just be as reckless as he used to be.
The 'bakudeku bakugou gets a spanking fanfic' could potentially be a story that plays with power dynamics. Bakugou is a very strong - willed character. So getting spanked could be a way to show his vulnerability. It could also be related to a bet or a dare in the fanfic's plot. Maybe Deku has something to do with it, either as the one who administers the spanking or as a witness to an event that leads to Bakugou getting spanked. But again, this is all speculation without actually reading the fanfic.
One possible plot could be that Bakugou is in the middle of a battle with villains. He's being his usual brash self, charging ahead. Suddenly, a sniper from the villains' side takes aim and shoots him. His friends then have to rush to his aid and figure out how to get him medical help while still fending off the villains.
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.
Well, Bakugou might struggle to control One for All at first. It's a powerful quirk and he has his own explosive temper. He could accidentally cause a lot of destruction while trying to master it.
One possible plotline could be Bakugou's journey to redeem himself after the expulsion. He might have to face his own flaws and work hard to prove that he can change. Another could be how his friends react to his expulsion, some might be shocked while others might try to help him get back in. Maybe there's a plotline where he discovers a new power or ability during his time away from school that makes him even stronger when he eventually returns.
There's also a possibility that it's an agent of a secret organization. This organization might be aiming to disrupt the hero society, and they see Bakugou as a key figure to target. So they send one of their best shooters to take him down.