One scenario could be that Draco witnesses Hermione being bullied by some Death Eater - sympathizing students. He steps in and uses his quick wit and knowledge of magic to outsmart them. Another could be in a situation where Hermione is being wrongly accused of a crime and is facing abuse in the form of unjust imprisonment. Draco, having some influence in the Ministry due to his family, intervenes and clears her name.
One possible scenario could be that Ron says something really mean to Hermione during an argument, and Draco, who has secretly been observing Hermione's intelligence and kindness, steps in to defend her. Maybe he uses his quick wit to shut Ron down verbally.
Well, Draco could save Hermione from abuse in fanfiction by first recognizing the signs of her abuse. Then, he might secretly provide her with protective spells or magical items. For example, he could give her a charmed amulet that wards off dark magic and physical harm. He also might use his knowledge of the Dark Arts to counter any curses or hexes that the abusers might use against her.
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 could be that in this fanfiction, Harry discovers that Hermione is being bullied by some dark - minded students at Hogwarts. He steps in immediately, using his skills and the respect he has among his peers to put an end to it. Maybe he threatens the bullies with exposure to the professors if they don't stop.
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 scenario could be a competition gone wrong. For instance, if there's a ninja skills competition between Ino and Sakura and Sakura cheats or loses her temper when losing to Ino. She might then try to attack Ino, and Naruto would save Ino. Another could be a love triangle - related situation. If Sakura thinks Ino is stealing Naruto's attention, she could lash out at Ino, only for Naruto to intervene.
In some fanfictions, Naruto might team up with other unexpected characters. Say, he teams up with some of the Akatsuki members who have a vendetta against Pein for some reason. Together, they are able to save Jiraiya from Pein's clutches.
Another motive could be related to his complex relationship with Dumbledore. Dumbledore might have asked Snape to look out for Draco, and Snape, being obedient to Dumbledore in many ways, would do so to fulfill his request. Also, Snape might believe that protecting Draco is part of a bigger plan to maintain the balance in the wizarding world.
Draco might be motivated by jealousy. He could be jealous of Ron and Hermione's friendship or a possible romantic relationship between them. So he tries to harm Hermione out of spite.
One reason could be Snape's sense of justice. Despite his often - cold exterior, he might not tolerate Draco's bullying behavior towards Hermione.