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.
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.
His expulsion would have a huge impact on Midoriya. Since they have a long - standing rivalry, Midoriya might feel a sense of guilt, as if he could have done something to prevent Bakugou from getting expelled. He might also be more determined than ever to prove himself, now that his main rival is no longer in the school environment.
Perhaps Bakugou gets expelled due to his attitude problems. He might have continuously bullied a fellow student to the point where the school can't overlook it anymore. His explosive temper could lead to him saying or doing something really offensive to a teacher or a large number of students, which would be against the school's code of conduct.
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.
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.
One interesting 'izuku gets expelled' fanfiction could be where he gets expelled due to false accusations of cheating. In this story, villains frame him to get rid of a potential threat. Another might be a story where his quirk goes out of control during a test and the school, in a panic, expels him. There could also be a fanfic where a jealous classmate sets him up to look bad and get expelled.
Well, one possibility could be that Mineta's inappropriate behavior finally catches up to him. Maybe he makes one too many lewd comments or actions towards his female classmates, and the school decides it's enough. So he gets expelled.
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.
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.