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.
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.
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.
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).
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.
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.
Snape, being a skilled wizard, could use magic to protect Draco. He might cast protective spells around Draco when he's alone or in vulnerable situations. Maybe he uses a spell that alerts him whenever Draco is in danger, so he can rush to his aid immediately.
One possible motivation could be that Draco has changed. He might have seen the error of his ways and decided to do the right thing. Another motivation could be that he has feelings for Hermione, even if they are not fully realized yet. He doesn't want to see her in a bad situation, so he steps in.