Perhaps the Death Eater is actually a childhood friend of Hermione's who got caught up in the wrong crowd. Hermione feels a sense of loyalty and responsibility towards him. She uses her knowledge of magic, especially things like memory charms and protective spells, to help him break free from the Death Eater's mindset. She might also have to face opposition from some members of the Order who don't trust the Death Eater, but she stands her ground and manages to successfully help him defect.
One possible plot could be that Hermione discovers a Death Eater who has doubts about Voldemort's cause. Maybe the Death Eater has a family member who was unjustly punished by Voldemort. Hermione, being the intelligent and empathetic witch she is, offers the Death Eater a way out. She could provide a safe haven or help them fake their death and start a new life away from the Dark Lord's influence.
Hermione would use her vast knowledge of magic. For example, she could use concealment charms to hide the Death Eater from other Death Eaters who might be looking for him. Also, she might use polyjuice potion to disguise him if they need to move around in public.
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.
Well, the Death Eater might save Hermione from a dangerous situation. For example, if she's captured by other dark wizards, the Death Eater could use his influence within the dark side to free her. This would be a huge shock to Hermione and the other characters, and it would lead to a lot of mistrust initially.
One possible fanfiction could be where the Death Eater is secretly an undercover agent for the Order. He helps Hermione by providing crucial information about Voldemort's plans. This could add a whole new layer of intrigue to the story as Hermione has to decide whether to trust this unexpected ally.
It could be about Hermione facing challenges from a Death Eater while dealing with the slur of being called 'mudblood'. Maybe the Death Eater tries to capture her for some dark purpose, and Hermione has to use her intelligence and magic skills to outwit the enemy.
It could be about Hermione somehow influencing a Death Eater to change their ways. Maybe she uses her intelligence and magical skills to show the Death Eater the error of their beliefs. For example, she might expose the true nature of Voldemort's regime which is based on fear and oppression, making the Death Eater question their loyalty.
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.
One possible plot twist could be that the Death Eater she marries is secretly a double agent. He might be working against Voldemort from within the Death Eater ranks and Hermione discovers this. Their relationship could start as a way to get closer to the Death Eater secrets but then turn into real love.
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.