In some fanfictions, a shared secret or a common goal can bring them together. For example, they might both be after a certain magical artifact, and during their search, they start to understand each other. The Death Eater could see Hermione's bravery and Hermione could see a glimmer of good in him. This gradually develops into love. It's a complex process that involves a lot of character growth for both of them.
The relationship could also develop from a situation of capture. Maybe the Death Eater captures Hermione but instead of harming her, he is intrigued by her. As she tries to escape, he finds himself more and more drawn to her. Their relationship then builds as they have intense conversations about their different worlds and values, and eventually, love might blossom in this strange and tense situation.
Well, it could start with the Death Eater being assigned to spy on Hermione or something related to the Order of Phoenix. As he gets closer to her, he starts to see her in a different light. He might be attracted to her intelligence first. Then, as they interact more, he realizes his feelings are deeper.
Over time, small acts of kindness can further the relationship. For instance, the werewolf might protect Hermione from other dark creatures without really thinking about it, and Hermione might use her magic to ease the werewolf's pain during his transformations. As they continue to interact in this way, their relationship can gradually shift from hostility to mutual respect, and potentially even to a deeper emotional connection like friendship or something more, but it has to be a very slow and gradual process to be realistic.
The plot could start with Hermione and the Death Eater being in a tight spot, facing the wrath of the wizarding community. Then, they could discover a common enemy who framed them. For example, a powerful dark wizard who wants to stir up chaos. As they work together, Hermione could use her knowledge of spells and potions to find clues, while the Death Eater might have some insider knowledge of the dark side's workings that helps them.
Hermione's character could be developed by showing her internal struggle. If she has a pureblood connection to Death Eaters, she might question her own identity. For example, she could struggle with the dark side of her family history while still holding onto her values of justice and knowledge.
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.
In the fanfiction, to develop their relationship, Hermione could first study about wolves in general and the magical aspects related to this particular wolf. This knowledge would help her approach it in a more understanding way. They could bond over a common goal, such as finding a lost magical artifact that the wolf seems to be guarding. As they search together, they learn about each other's strengths and weaknesses. Hermione might also use her empathy to understand the wolf's feelings, which deepens their connection.
It might be portrayed as a tense encounter. Hermione would be on her guard, ready to use her magic if necessary. The Death Eater, on the other hand, could be sneering and full of dark arrogance.
Their relationship could start with hostility. Lucius might initially try to undermine Hermione's efforts in some wizarding matter, but she outsmarts him every time. This could gradually turn into a begrudging respect as he realizes her intelligence. For example, in a magical research competition.
The relationship could develop through mutual respect for each other's intelligence. Snape respects Hermione's academic prowess and Hermione comes to respect Snape's deep knowledge of magic. For example, in a situation where they are working on a difficult potion together, they start to see each other's strengths.
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.
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.