It could be All For One. He's a powerful and menacing villain in the My Hero Academia universe. Since Kurogiri is saving Deku, All For One might be trying to target Deku for his own purposes, like stealing his quirk or using him as a pawn in his grand scheme to take over the hero society.
A prevalent theme is loyalty. Whether it's his loyalty to the League of Villains or the possibility of a shift in loyalty. Also, the theme of power and how Kurogiri's unique powers are used or developed in different scenarios is quite common in these fanfics.
One great 'bnha kurogiri fanfic' is 'Kurogiri's Redemption'. It explores Kurogiri's character in a unique way, showing his potential for change. Another is 'Kurogiri: The Hidden Past' which delves into his backstory and how he became who he is in the BNHA universe.
One possible plot for this fanfiction could be that Deku is facing a powerful and unknown enemy that has the ability to nullify his powers. He's in a desperate situation when Kurogiri shows up. Kurogiri, for reasons unknown to Deku at first, uses his portal - creating abilities to rescue Deku. It could turn out that Kurogiri has a connection to Deku's past that he's not aware of. Maybe Kurogiri was once influenced by someone who saw the same kind of potential in Deku that he himself had when he was younger, and that's why he saved him.
The students of Class 1 - A are often involved. For instance, Midoriya might be portrayed as being unjustly treated by Aizawa, and the fanfic could focus on Midoriya's struggle against Aizawa's supposed unfairness. Bakugo could also be in the story, maybe being in conflict with Aizawa's disciplinary actions.
Aizawa is still going strong in the manga. There's no event or storyline that has resulted in his death. The creators have chosen to keep him as an active character.
Another good place is FanFiction.net. It's been around for a long time and has a significant amount of My Hero Academia content. When searching for Kurogiri fanfiction, be sure to read the summaries and reviews to get an idea of the quality and content of the story. Some stories might focus on his backstory, while others could explore his relationships with other characters in the series.
First, understand Kurogiri's character. He's mysterious and has a unique power in the My Hero Academia universe. Research his actions, dialogues, and relationships in the original series. This will help you write him in - character. For example, his loyalty to the League of Villains is an important aspect to consider.
Aizawa may also interact with Izuku's family during family events or gatherings in the fanfic. He could be a guest and during that time, he could share his insights on Izuku's growth and development. This would not only strengthen his relationship with Izuku but also with his family as a whole.