Perhaps he owes her a debt. In the story, Hermione could have saved his life or the life of someone he cares about. This debt of gratitude then compels him to protect her. It could also be that he is trying to use her protection as a way to gain favor with the side of good, hoping for a pardon for his past deeds as a Death Eater.
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.
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 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.
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.
One reason could be to add more conflict within the Weasley family. Percy was already somewhat of an outcast in the family due to his loyalty to the Ministry. Turning him into a Death Eater would intensify that divide.
One possible plotline could be that the so - called Death Eater is actually an undercover agent for the good side. Hermione gets involved with him not knowing his true identity at first, and as they get closer, she discovers the truth. Their relationship then becomes a complex mix of love and the fight against the real Death Eaters.
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.
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.
In this type of fanfiction, the relationship between Hermione and the Death Eater could be very complex. Maybe it starts as a hostile one, but as the story progresses, they might find some common ground or mutual understanding. It could also be a story of redemption for the Death Eater through Hermione's influence.
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.