One common theme is redemption. Snape often has to atone for his past behavior towards Harry, and taking him in is a step in that direction. It's about him becoming a better person in the face of Harry's need for care.
I really like 'Under Snape's Wing'. It starts with Harry being in a really bad state from the abuse he has endured. Snape, with his own set of issues, takes Harry in. The story follows their journey as they learn to co - exist, with Snape slowly becoming a protector figure for Harry. It's full of heart - warming moments as well as some tense ones as they navigate their new relationship.
One possibility could be that in this fanfiction, Snape takes Harry for some sort of training or protection. Maybe Snape realizes that Harry is in greater danger than Dumbledore anticipates and decides to take matters into his own hands. He might take Harry to a secret location to teach him advanced magic or to keep him away from the prying eyes of Voldemort's followers.
In the fanfiction, Snape might take Harry because he discovers a connection between Harry and an ancient magic that could be dangerous if misused. So, he takes Harry to a place where he can keep an eye on him and make sure the magic is not exploited by the wrong people.
One common theme is redemption. Even though Snape is abused, the story might lead to a path where he finds some form of redemption or peace. Another theme could be power struggle. With Snape being in a position of power at Hogwarts but also being a victim of abuse, the power dynamics are often explored.
Yes, there are some. You can start by looking on fanfiction platforms like Archive of Our Own. There you might find stories that explore the concept of Snape being abused in the context of the Harry Potter universe. However, the quality can vary widely, so it might take some time to sift through and find ones that really capture your interest.
There's a fanfic titled 'Snape's Redemption in Harry's Abuse'. This story focuses on how Snape, who has his own complex past with Harry's father, realizes that Harry is a victim of constant abuse. He decides to use his position as a teacher and his skills in potions and magic to keep Harry safe. It delves deep into the relationship between Snape and Harry, exploring themes of forgiveness and second chances.
One place to start looking could be on fanfiction platforms like Archive of Our Own (AO3). Just use the search function and type in 'Snape comforts abused Harry Potter'. There are often filters you can use to further refine your search, like by rating, word count, etc.
Snape's reaction could be quite mixed. On one hand, he might be angry at Dumbledore for not doing more if he knew about the abuse. He may also feel a strange sort of empathy towards Harry. After all, Snape himself had a difficult childhood. So, he could start to be a bit more lenient with Harry in his classes and try to subtly offer support.
In some versions, Snape might notice Harry's withdrawn behavior or signs of physical harm during Potions class. Maybe Harry flinches when someone gets too close, which makes Snape suspect something is wrong.