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.
It could also be that they are initially enemies within the Death Eater world. But as they witness the atrocities committed by the Death Eaters, they both have a moment of realization. Draco, having grown up in that world, and Hermione, seeing it from an outsider's perspective. This shared experience could lead to a begrudging respect that then blossoms into a deeper relationship as they try to find a way out of the dark world they've found themselves in.
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.
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.
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.
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.
One idea could be that Draco and Hermione are forced to work together undercover among the Death Eaters. They start off distrusting each other but as they face various challenges within the Death Eater ranks, they begin to understand each other better. For example, they might have to find a way to stop a particularly heinous Death Eater plan while pretending to be on their side.
A possible plot twist could be that Hermione gets turned into a Death Eater against her will, and Draco has to help her break free from the dark magic controlling her. This would completely reverse their typical roles.
In some fanfictions, Hermione as a Death Eater is a very interesting and often controversial portrayal. Sometimes, it might show her being forced into the role due to some dark magic or blackmail. This completely flips her good - girl image from the original series and allows for a very different exploration of her character.