Well, perhaps Fenrir Greyback is not as completely evil as he seems in the original story. In this fanfiction, he might be helping Hermione escape because he has a debt to pay to someone who cares about Hermione. Or, he could be trying to make amends for some of his past misdeeds in a very strange way. It's also possible that he has been influenced by some external magical factor that makes him act out of character.
One possible reason could be that he has some sort of hidden agenda. Maybe he wants to use Hermione as a bargaining chip later. Another reason might be that there is some magic or force compelling him to do so against his will. It could also be that he has a momentary change of heart, perhaps seeing something in Hermione that reminds him of a past acquaintance or a long - lost bit of humanity within himself.
Well, perhaps in the fanfiction, Fenrir Greyback is under the command of Voldemort to watch Hermione as she is seen as a threat to the Dark Lord's plans. He might follow her around Hogwarts, observing her every move. This could lead to some tense moments where Hermione senses she's being watched but can't quite figure out who it is at first. As the story progresses, she could start to set traps to catch her stalker, which would be Greyback. And there could be a big showdown between them in the end.
One possible consequence could be her transformation into a werewolf. In many werewolf lore within the Harry Potter universe, a bite from a werewolf like Fenrir Greyback often leads to lycanthropy. This would mean that Hermione would have to deal with the monthly transformations, and she would likely face discrimination from some in the wizarding world who are prejudiced against werewolves.
One possible reason could be his Slytherin pride and the long - standing rivalry between Gryffindor and Slytherin. He might have said something mean to Hermione in the heat of that rivalry. Another reason could be jealousy. Maybe Hermione is achieving more academically or getting more recognition, and Draco, being a proud pure - blood, can't stand it.
One possible theme is redemption. Maybe the fanfiction explores the idea of Greyback being redeemed through his interaction with Hermione. This could be appealing as it shows the power of goodness (represented by Hermione) over evil.
One possible plot could be that Fenrir, for some reason, has a change of heart. Maybe he sees Hermione's kindness and intelligence during one of his encounters with the wizarding world. He starts to protect her secretly from other dark forces. And Hermione, initially afraid, gradually realizes there's more to him than just a monster.
One possible plot could be that Hermione stumbles upon Fenrir Greyback in a situation where he's about to be killed by some dark wizards who see him as a loose end. Hermione, being the empathetic and brave witch she is, decides to save him. Maybe she believes that every life is worth saving, even a werewolf like Fenrir. She could then try to rehabilitate him, using her vast knowledge of magic and her strong moral compass.
I'm not sure if there is such a specific fanfiction. It seems like a rather dark and unusual pairing considering Fenrir Greyback is a werewolf known for his brutality. However, the world of fanfiction is vast, and there might be some out there that explore this concept, but it's not a common or mainstream idea in the Harry Potter fanfiction community.
One possible plotline could be that Fenrir takes Hermione as a hostage to use against the Order of the Phoenix. He might think that her connection to Harry Potter makes her a valuable bargaining chip. Another could be that he is under the control of a dark wizard who orders him to capture Hermione for some dark magic ritual. In some fanfictions, it could also be that Fenrir has some sort of personal vendetta against Hermione and takes her to exact revenge for something she did to him or his kind in the wizarding war.
Their relationship could start with Hermione being a captive of Fenrir. But instead of harming her immediately, he becomes intrigued by her intelligence. As time passes, Hermione might start to see some humanity in Fenrir that others don't, and they could form an unlikely alliance against a common enemy.
One possible plot could be that Fenrir Greyback, for some reason against his usual nature, discovers Hermione in a vulnerable state. Maybe she's been separated from her friends during a battle. He decides to keep her safe from other dark creatures, seeing some sort of potential in her that he doesn't want wasted. He might teach her some of the ways to survive in the wild, which are skills he has as a werewolf.