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.
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 '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.
Well, it could be that Draco is forced to follow the Death Eater path while Hermione is fighting against them. But then, they might get thrown into some situations together, like being trapped in a place. Draco realizes that Hermione is not just a Mudblood in the sense that he was taught, and they start to form an unlikely bond. Their relationship could be full of tension, with Hermione constantly trying to convert Draco or at least make him see the wrong in what he's doing, and Draco struggling between his loyalty to his family's Death Eater ideals and his growing feelings for Hermione.
One interesting Death Eater fanfiction could be about a young wizard who is forced to join the Death Eaters but secretly tries to undermine them. For example, they might be passing information to the Order of Phoenix.
One possible scenario in such a fanfiction could be that Sirius is somehow forced or tricked into becoming a Death Eater. Hermione might then try to rescue him from the dark side. Maybe she discovers some ancient magic that can reverse the dark mark's influence on him.
It's a very controversial topic. In the Harry Potter universe, the term 'Mudblood' is a highly offensive slur used by Death Eaters and those with pure - blood supremacist views. Writing a fanfiction about such a relationship might be seen as glorifying or normalizing such a discriminatory ideology. However, if the fanfiction is used as a means to explore themes of redemption, changing views, or challenging such bigotry, it could be done in a more acceptable way.
Another theme might be the power of knowledge. Hermione is known for her academic prowess. In fanfiction, this knowledge could be the key to either defeating the Death Eater or changing their views. For instance, she might use her knowledge of ancient magic to counter the dark magic of the Death Eater.
Snape could be very cautious in his interactions. He would be constantly aware of the power dynamics. He might flatter the more powerful Death Eaters subtly to avoid suspicion. For instance, he could compliment Bellatrix on her loyalty to the Dark Lord. At the same time, he might try to intimidate the weaker ones to show that he's not to be trifled with. He might use his knowledge of the Dark Arts to his advantage in these interactions, like casually mentioning a difficult spell he's mastered to gain some respect.
Another plotline could involve the Mudblood initially being terrified of the Death Eater due to their reputation. But as the story progresses, she might see the good in him and start to fall in love too. Their relationship could then be a story of overcoming differences and prejudices. For instance, they might have to face opposition from both the wizarding world that hates Death Eaters and the Muggle - born community that is suspicious of the Death Eater's motives.