In fanfiction, Draco may save Hermione from Greyback because he has developed some feelings for her. These feelings might have been growing slowly over time as he saw her in different situations at Hogwarts. When it comes down to it, he can't bear to see her hurt by Greyback. Also, he could be trying to make amends for his past actions. Saving Hermione could be his way of starting to redeem himself in his own eyes and in the eyes of others. It's a big step towards changing his image from a typical Slytherin bully to someone with a bit of a heroic side.
One possible motivation is a sense of morality that Draco has buried deep inside. Despite his upbringing in a family of Death Eaters, he still has a conscience. Seeing Greyback about to harm Hermione, who is essentially an innocent in the face of such a brutal werewolf, stirs that conscience. Another factor could be his own self - interest. He might realize that by saving Hermione, he could gain some sort of leverage or protection in the complex world of the wizarding war.
Love. In fanfictions, it's a common motivation. Draco might have fallen in love with Hermione over time, and that love drives him to risk his life to save her from Voldemort.
One reason could be Snape's sense of justice. Despite his often - cold exterior, he might not tolerate Draco's bullying behavior towards Hermione.
It could be out of loyalty to the wizarding world. Harry is seen as an important figure in the fight against the dark forces. Fleur realizes that Harry's safety is crucial for the future of the wizarding community, so she saves him from the Dursleys who are a threat to his well - being in a different way compared to the dark wizards.
Draco could be seeking redemption. He may be tired of being on the wrong side of the war. Saving Hermione, who is a symbol of the good side, would be a significant step in his journey towards redemption. Additionally, he might be influenced by his friendship or alliance with some of the other characters who are on the side of the Order of the Phoenix. They could have convinced him to do the right thing and save Hermione from Bellatrix.
One motivation could be that Draco has developed feelings for Hermione. So, when he sees Viktor as a rival for her attention or a threat to her safety, he takes action to save her.
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.
In many fanfictions where Draco saves Hermione from Greyback, it often starts with a situation where Hermione is in immediate danger from Greyback. Draco, perhaps having a change of heart from his Slytherin ways, decides to intervene. He might use his knowledge of the Death Eaters' plans or the layout of the area to his advantage. For example, he could lead Hermione to a secret passage that Greyback doesn't know about. This event can be a turning point in their relationship, leading to a newfound respect and sometimes even the start of a romantic connection between them, as they both realize there is more to each other than they initially thought.
Stiles is a very loyal friend. He would see Erica and Boyd in trouble and feel compelled to help. In the show, he has always been there for his friends, and this would carry over into the fanfiction. He can't stand by while Gerard does something bad to them.
His sense of justice. Power Rangers are all about doing what's right, and saving a life in danger is a top priority for them.
Well, you could check out 'The Unexpected Hero'. In this fanfic, Draco steps in and saves Hermione from the troll in a rather dramatic turn of events. The author does a great job of building the tension and making the rescue scene exciting.