One common theme is redemption. The Death Eater often has a chance to redeem themselves through saving Hermione. It shows that even those on the 'wrong side' can turn things around.
Another one is 'The Unlikely Protector'. Here, a Death Eater saves Hermione when she is on a dangerous mission. The story focuses on the internal struggle of the Death Eater, who has to deal with the expectations of his fellow Death Eaters while also trying to keep Hermione safe. It's an interesting read that plays with the idea of good and evil not being so black and white.
It changes the storyline by introducing an unexpected ally. Hermione, who was used to seeing Death Eaters as pure evil, now has to reevaluate her views. This can lead to new alliances and different ways of fighting against Voldemort. For example, she might use the Death Eater's inside knowledge of Voldemort's plans.
Well, I've read a few. There's this one where the Death Eater saves Hermione from a group of rogue Dementors. It was really interesting how the author explored the idea of redemption for the Death Eater. Then there's another where the saving happens during a battle at Hogwarts. The Death Eater, who had been secretly having doubts about Voldemort's cause, decides to act and rescue Hermione. It was a great read as it delved into the complex nature of the characters. There's also a more recent one that shows the aftermath of Hermione being saved, like how she has to deal with the wizarding world's reaction to a Death Eater doing a good deed.
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.
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.
Another idea could be that she is somehow brainwashed. There could be a dark spell or a powerful magical object that alters her perception and makes her believe in the Death Eater ideology. In this scenario, her friends would have to find a way to break the spell and bring her back to her true self.
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.