One consequence could be that Hermione gains a new ally in Snape. Snape, being a powerful and knowledgeable wizard, could offer her guidance and access to knowledge that she wouldn't otherwise have. He might share some of his more advanced potions techniques or insights into the dark arts (for the purpose of defense, of course). This could enhance Hermione's own magical abilities and her standing within the wizarding community.
She might use her extensive knowledge of magic. For example, she could brew a complex potion that cures a deadly curse Snape has been afflicted with. Hermione is known for her academic excellence in potions, so it's very likely she'd use this skill to save him.
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).
One possible scenario is that Snape steps in during a confrontation. Bellatrix is about to harm Hermione, and Snape, using his quick reflexes and advanced magic, stops her. He could be acting out of his own sense of right and wrong, or perhaps because he has a hidden agenda that involves keeping Hermione safe.
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.
The theme of sacrifice also appears. Snape may have to sacrifice his own safety, reputation or his standing within the wizarding world to save Hermione. This shows his selfless side that might have been hidden before. And in some fanfictions, this sacrifice is what ultimately changes the course of the story and the characters' development.
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.
The Dursleys might be left in a state of shock and confusion. Since they have been so mean to Harry, they could be worried that the wizarding world will come after them for revenge. But since they are Muggles, the wizarding world may just leave them be, but they will always live in fear of the unknown.
They might face magical justice. In some fanfictions, the Ministry of Magic could get involved and strip them of their magic, or at least put them under strict surveillance.
One popular 'snape saves hermione fanfiction' is 'A Different Perspective'. In this story, Snape's complex character is explored in the context of saving Hermione from a dangerous dark magic situation. It delves into his motives which are a mix of his loyalty to the light side deep down and his growing respect for Hermione's intelligence and courage.
In fanfiction, Snape saving Harry often showcases a complex side of Snape's character. It might be a redemption arc for him, as in the original series, Snape had a very ambiguous relationship with Harry. In these fanfictions, it could be due to his love for Lily that he finally decides to fully protect Harry, which is a very interesting take on his character.