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 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.
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.
In such a fanfiction, Hermione might initially be in great danger. The Death Eater could try to capture her to use as leverage against Harry Potter. Maybe she uses her quick wits and vast magical knowledge to outsmart the Death Eater at first encounter.
Another idea is that Sirius, as a Death Eater, has some information that Hermione needs to defeat Voldemort. She has to convince him to give it to her while also dealing with his newfound allegiance. It could be a race against time as other Death Eaters suspect Sirius of being unfaithful to their cause, and Hermione has to protect him while also getting the crucial information.
In some fanfictions, Hermione might be a Death Eater spy due to a complex backstory. Maybe she was blackmailed. For example, if the Death Eaters threatened to harm her Muggle - born parents, she could be forced to spy for them. This would be a huge deviation from her canon character, but in the realm of fanfiction, it allows for exploring different character arcs and moral dilemmas.
Well, one possibility is that Hermione uses her quick wits and magic skills to defend herself. She might immediately cast a stunning spell or a protective charm. For example, she could use the Protego spell to create a shield between her and the Death Eater. Then, she would likely try to find a way to escape or call for help. Maybe she'd use her Time - Turner (if she still has it in the fanfiction context) to go back a few minutes and avoid the encounter altogether.
Well, one possibility is that Hermione uses her intelligence to outwit the escaped Death Eater. Maybe she sets up a series of magical traps. She could use her knowledge of spells like the Stunning Spell or the Binding Charm to keep the Death Eater at bay until help arrives.
In fanfiction, when Hermione talks to a Death Eater, she might try to persuade the Death Eater to abandon their dark ways. For example, she could use her intelligence and knowledge of the wizarding world to show the Death Eater the error of their beliefs. Maybe she would bring up the harm that Voldemort has caused and how following him is only leading to destruction.
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.