Authors often portray it as a very antagonistic relationship. Fenrir is a dark and violent character, and Hermione is a symbol of good and knowledge. So, their interactions are usually filled with tension, like Fenrir seeing Hermione as a target because of her connection to Harry Potter and the fight against Voldemort.
In some fanfictions, the relationship is portrayed as one of pure enmity. Fenrir Greyback, being a cruel and savage werewolf, is seen as a threat to Hermione. He represents the dark and violent side of the wizarding world that she is constantly fighting against. His predatory nature towards her, especially given her Muggle - born status, makes for a very tense and hostile relationship.
Their relationship might develop through a series of tense encounters. Fenrir might be initially attracted to Hermione's magic and her strong will. As they interact more, Hermione could start to see a glimmer of humanity in Fenrir, despite his monstrous actions. This could lead to a complex relationship where she tries to reform him in some way, while he struggles with his dark nature and his growing feelings for her.
You can start by looking on popular fanfiction websites such as Archive of Our Own (AO3). AO3 has a vast collection of fanfictions from various fandoms, and there's a good chance you'll find some Hermione Granger x Fenrir Greyback stories there. Just use the search function and type in the relevant tags.
Hermione would likely react with her characteristic intelligence and courage. She would probably try to use her vast knowledge of magic to find a way to escape or at least resist Fenrir. For example, she might try to use spells that could incapacitate him temporarily. She would also be likely to try and outwit him in conversation, looking for any weaknesses or loopholes in his plans.
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.
For Hermione, her development could involve facing her fears of werewolves like Fenrir. She might start off being very cautious and perhaps a bit prejudiced due to his reputation. But as the story progresses, she could learn to look beyond the surface and see the complex person (or creature) that Fenrir is. This would show her growth in empathy and open - mindedness.
There could also be a fanfiction where Hermione Granger is forced to face Fenrir Greyback alone in a dangerous situation. This would showcase her bravery and her ability to use her magic skills under extreme pressure. The story could focus on her mental and magical struggle against Greyback, perhaps with her using some of the more advanced spells she has learned over the years to defend herself and those around her from the werewolf's attacks.
One interesting storyline could be Hermione using her intelligence to outwit Fenrir Greyback. For example, she could create a spell or potion that repels werewolves like him. Another could be a scenario where Fenrir tries to capture Hermione for some dark purpose, but she manages to turn the tables on him with the help of her friends. Maybe she could also find a way to cure Fenrir's lycanthropy, leading to a change in his character.
One interesting plot could be Hermione trying to use her intelligence to outwit Fenrir Greyback. Maybe she's on a mission to rescue someone he's captured, and she has to use her magic skills in new and creative ways. For example, she could use a combination of transfiguration and charms to create distractions while she sneaks around his lair.
Often, they portray it as a very deep and trusting friendship. Since they have been through so much together in the original series, fanfiction writers like to expand on that. They might show how they support each other during tough times at Hogwarts, like when dealing with difficult exams or mean classmates.