One possible reason could be that Snape sees Hermione's value as a brilliant student. He might recognize her potential and not want it to be wasted just because of her dad's actions or situation. Maybe he has a sense of justice deep down, despite his often cold exterior.
He could use his position of authority. Snape might confront the abuser directly. Since he's a teacher, he has the power to intimidate and put a stop to any immediate harm. He could also give Hermione a safe place to stay, like his own quarters (if it's within the rules of the fanfiction world).
Well, Hermione might be initially distrustful of Snape. After all, he has a reputation. But as time goes on, she could start to see his good side. They might form an unlikely alliance. Snape could use this opportunity to teach Hermione some advanced magic that she wouldn't have learned otherwise.
In many fanfictions, Snape saving Hermione from Voldemort can be a very interesting plot. It could be due to Snape's complex character. He was a double - agent in the original series. So, in fanfiction, his loyalty to Dumbledore might drive him to protect Hermione, who is an important part of the good side against Voldemort.
Well, perhaps Snape uses his position as a teacher to step in. He could have been observing the situation secretly and when Draco was about to do something harmful to Hermione, Snape intervened with a firm command or some magic spell to stop Draco in his tracks.
Well, it could be that Snape has been secretly observing Ron's erratic behavior towards Hermione. When the situation gets out of hand, he intervenes. He might use his position as a teacher to discipline Ron and in the process, saves Hermione. Snape is a complex character with a lot of power and knowledge, so he could use various means like his occlumency skills to sense the danger Hermione is in and act accordingly.
One reason could be Snape's sense of justice. Despite his often - cold exterior, he may not tolerate Ron's unjust behavior towards Hermione. Another reason might be that he sees something in Hermione that he values, like her intelligence or her thirst for knowledge, and doesn't want it to be extinguished by Ron's actions.
Well, it could be that Draco, in his pure - blood pride and influenced by his family's views, targets Hermione. Maybe he uses some dark magic or just plain bullying. Snape, despite his often cold exterior, might save her because he secretly admires Hermione's intelligence or perhaps he has a deeper reason related to his own past with the Gryffindors or his hidden loyalties. For example, he could see a bit of himself in Hermione's determination to succeed in a world that is often against her.
Snape would probably be very stern with Draco. He might give him a severe scolding and deduct points from Slytherin. Snape is a strict teacher and he won't tolerate such behavior from his own house students.