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.
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.
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).
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.
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.
Luke might become more enraged. Since Percy has thwarted his plan to do something to Annabeth, he could seek revenge. He might start plotting more devious schemes against Percy and Annabeth, or even their friends.
She might be in shock at first. After all, she was in a life - threatening situation. But then she could feel extremely grateful towards Edward and their relationship might grow stronger.
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.
After saving Harry, Snape may have to deal with a lot of mistrust from some people in Hogwarts who don't understand his motives. However, he might also start to form a closer bond with Harry, which could change the whole dynamic between them. This new relationship could lead to some unexpected alliances and enmities within the wizarding world. And if the Dursleys were to try and retaliate, Snape would have to constantly be on guard to protect Harry from any potential harm they could cause.
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.