Redemption. He wants to make up for all the bad things he has done as a Death Eater. Protecting Hermione, a key figure in the fight against the Dark Lord, is his way of seeking redemption. He hopes that by doing this, he can atone for his past sins.
A sense of justice. The Death Eater might start to question Voldemort's ideology. He sees Hermione as an innocent being persecuted just because of her birth. His long - buried sense of justice resurfaces and he decides to protect her.
Love. Maybe the Death Eater has fallen in love with Hermione secretly. It could be her intelligence, her bravery, or her kindness that attracts him. And this love overcomes his loyalty to the Death Eaters and the dark side.
It could be someone who has a hidden good side, like Draco Malfoy. He was from a Death Eater family but showed signs of not fully embracing the dark side. Maybe in this fanfiction, he decides to protect Hermione for some unforeseen reason, perhaps because he has developed a new understanding of the value of life and friendship.
Another possibility is that he is in love with her. In fanfiction, love can be a powerful motivator. He might be attracted to her intelligence, her strong will, and her beauty. This love could override his loyalty to the Dark Lord and make him want to protect her at all costs. He could see her as a symbol of hope and a better future for the wizarding world.
It could also be that Hermione is on a mission to gather information. By helping the Death Eater, she hopes to gain insider knowledge about the Death Eater's group or their plans. This would be a strategic move on her part, using the situation to her advantage in the fight against the dark forces.
Bellatrix Lestrange is also a likely candidate. Her encounter with Hermione would be extremely intense. Given her loyalty to Voldemort and her rather unhinged nature, she would likely pose a serious threat to Hermione, but Hermione might also find a way to use Bellatrix's madness against her.
Bellatrix Lestrange's younger brother or some other minor Death Eater character could be used. This would allow for the creation of a new character with his own motives and backstory. He could be betrothed to Hermione as part of a larger plot by Voldemort to gain control over Hermione's knowledge and magic. This would put Hermione in a very difficult position as she would be tied to a very dark and dangerous family.
There's also a possibility that it could be a minor Death Eater that we don't know much about from the original series. The author of the fanfiction could create a new character who was a Death Eater but is now having doubts. Hermione could be the one to find this person and start their journey of change. This would give the author a lot of creative freedom to develop the character's backstory and their relationship with Hermione.
Perhaps it's because the fanfiction offers a different perspective on the Death Eaters. It might show their motives or backstories in a new light that Hermione, being the inquisitive person she is, finds fascinating.
One possible motive could be a deep - seated dissatisfaction with the wizarding world's status quo. Maybe she felt that the Ministry of Magic was corrupt and that the Death Eaters had a better vision for change, although a very dark one. Another could be some sort of personal vendetta against someone in the Order of the Phoenix or Hogwarts faculty that made her side with the Death Eaters.
It's a really strange concept. In the original 'Harry Potter' universe, Hermione is firmly on the side of good. But in fanfiction, if she's a Death Eater, it could be a result of a time - travel gone wrong. She might have made a different choice in an alternate timeline that led her down the dark path. But again, this is very much against the essence of her character.
Well, it could be due to a sense of hopelessness. If she feels like the good side is losing the battle against the Death Eaters and there's no other way to protect her friends and the wizarding world, she might think that joining them could give her some power to influence things from the inside. But of course, this would be a very dark path for her to take.