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.
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.
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.
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.
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.
There's 'The Unlikely Bond'. Here, the Death Eater, say Draco (as in some fanfictions he has Death Eater - like tendencies), falls in love with Hermione when they are paired for a school project. It shows how love can cross the boundaries of their different beliefs. Also, 'Shadow of Love' is a great one. The Death Eater is secretly protecting Hermione from the other dark forces, all because of his unspoken love for her.
One possible aspect of this fanfiction could be Hermione's encounter with an unexpected Death Eater. Maybe she stumbles upon one during a mission or while exploring a hidden area. This encounter could lead to a series of thrilling events, like a battle of wits or a dangerous duel.