She might be initially defensive. Hermione is a proud and independent character. So, when Snape finds out about her arm, she could be worried that he'll use it against her in some way, like taking away house points or using it as an excuse to give her extra work.
Maybe Snape uses this discovery as an opportunity to teach Hermione something new. He could be curious about how she got the condition on her arm and offer to show her a spell or potion to heal or manage it. This would also be a chance for him to show a different side of himself, not just the strict professor.
In the fanfiction world, if Snape found out Hermione had been raped, he might first be filled with a cold rage. He could use his skills and influence to seek out the perpetrator. Given his complex character, he would likely take justice into his own hands in a very Snape - like way, perhaps using his knowledge of the Dark Arts to exact revenge while also trying to protect Hermione from further harm and the public eye.
He would probably be very displeased. Snape has always been strict and traditional, and fanfiction about the DA, which was an unauthorized student group in his eyes, would seem like a frivolous and inappropriate thing to him.
Snape might be suspicious at first. He might think it's some sort of trick or part of a bigger plot. However, as he observes Hermione more closely and realizes the genuineness of her situation, his attitude could gradually change to one of reluctant assistance. He might even offer some words of wisdom, albeit in his typical sarcastic way, to help Hermione regain her strength.
One great fanfiction with this theme is 'Hermione's Pureblood Revelation' on FanFiction.net. It delves into how Hermione discovers her pureblood heritage and how it changes her relationships at Hogwarts. She has to deal with the new - found knowledge and the expectations that come with being a pureblood in the wizarding world.
Hermione's intelligence means she can quickly spot flaws in Snape's statements. So, she can correct him, which annoys him. For example, if Snape makes a small error in a potion ingredient amount, Hermione will point it out right away.
There could also be some unknown characters in the fanfiction. Maybe a secret society within Hogwarts that has been using the cupboard for their own purposes. When Hermione finds out about it, she gets caught up in their affairs. These unknown characters could be students from different houses or even former Hogwarts students who have come back for some hidden agenda related to the cupboard.
I recall a story titled 'Snape's Watchful Eye on Hermione'. It shows Snape noticing Hermione's potential early on. He starts leaving little hints and protective spells around her. The story also delves into Snape's complex feelings, as he sees a bit of himself in Hermione's thirst for knowledge and her outsider status among some of the Gryffindors.
A common theme could be redemption. Snape, who has a complex and often - dark past, might find in Hermione a chance to redeem himself in some way. Maybe he saves her from a danger in the dungeon, which starts his journey towards a more positive path. Another theme is the exploration of hidden knowledge. The dungeon is full of secrets, and both Snape and Hermione are curious minds. They could uncover something that changes their understanding of Hogwarts or the wizarding world.