Well, perhaps Hermione is captured during a battle. The Death Eaters, seeing her as a valuable asset, might find a way to bind her will. They could threaten her friends' lives to make her comply and be their slave. In the fanfiction, this could lead to a series of events where Hermione has to secretly fight against the control while appearing to be a loyal slave.
One way it could develop is through the use of dark magic coercion. Maybe a powerful Death Eater discovers Hermione's intelligence and decides to use Imperius Curse to make her his slave. He could force her to use her magic skills for his evil purposes, like brewing dangerous potions or stealing valuable magical artifacts.
Hermione could resist the Death Eaters with her vast knowledge of magic. For example, she could use protective spells and charms she has learned from her studies. She might also use her quick thinking to outwit them in verbal exchanges, not giving them any information or advantage.
In this fanfiction, Hermione could rehabilitate Death Eaters by showing them the error of their ways. She may expose them to the harm they've caused to both the Muggle - born and the wizarding community at large. By making them face the consequences of their actions on a personal level, like the families they've torn apart, she might start to change their views.
One way the storyline could develop is that Hermione would struggle with her identity. She might initially be in denial about her father's Death Eater past. For example, she could discover it accidentally and then have to face the prejudice from her friends at Hogwarts. This would create a lot of internal conflict for her as she has always been a defender of justice and against the Dark Arts.
The story could develop with Hermione trying to escape on her own. She might use her intelligence to find weaknesses in the Death Eater's security. For example, she could figure out the patterns of their patrols and use her magic to create distractions.
Well, in some fanfictions, Hermione might use her superior intellect. She could outwit the Death Eaters by setting up elaborate magical traps. For example, she could use transfiguration magic to create objects that suddenly turn into something dangerous when the Death Eaters approach. Another way could be through her extensive knowledge of potions. She might create a potion that incapacitates or kills them when they come into contact with it.
Well, in this kind of fanfiction, perhaps Hermione is captured because she was on a solo mission to retrieve some important magical item. The Death Eaters could use her knowledge to try and break into the secrets of the Order of Phoenix. Meanwhile, Hermione could be using her wits to delay them and send out hidden signals for help.
Well, she could end up in a duel with a powerful Death Eater. Hermione is a very skilled witch, so it would be a great show of her magical abilities. Maybe she discovers a new spell during the fight that helps her gain the upper hand.
If Hermione joined the Death Eaters in fanfiction, it would completely turn the original plot on its head. The Death Eaters are known for their dark magic and prejudice, which is the opposite of Hermione's values. This could lead to a very different kind of story, perhaps one where she tries to change the Death Eaters from the inside, or she could be a double agent. It would be a very dark and complex alternate universe.
Perhaps in the fanfiction, Hermione has something that the Death Eaters are after, like a powerful magical artifact. They fight over who gets to take her prisoner first in order to extract the location of this artifact from her. It could also be that they are under the orders of Voldemort to capture her alive, but they start fighting among themselves due to personal rivalries and the desire for glory within the Death Eater ranks.
A fanfiction involving Hermione and Death Eaters could focus on a moral dilemma. For example, if Hermione has the chance to save a Death Eater's life, would she do it? This could explore her character's sense of right and wrong. It could also be about how she endures the psychological torture that the Death Eaters might inflict on her, showing her strength and resilience.