In some fanfictions, Harry might face a situation where his near - death experience gives him new powers or insights. For example, he could have a vision during a brush with death that shows him the location where Hermione is in danger. Then he uses this knowledge to reach her in time and save her.
One way could be through the death of a villain. If a villain who was targeting Hermione dies, Harry no longer has to worry about that threat to her. Maybe the villain's death releases Hermione from a spell or trap she was in.
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.
A possible motive could be self - preservation. If they believe that Voldemort's downfall is inevitable and that by saving Harry, they can gain some form of leniency from the side that opposes Voldemort. They might think that Harry has enough influence to spare their lives if they help him.
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.
Maybe some of the Hogwarts professors like Professor Sprout. After all, she's the Herbology teacher. She could give Harry some expert advice on how to grow different kinds of food plants. She might even let him use some special greenhouses or tools in the school for his food - growing projects.
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 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.
A possible plotline could be that a Death Eater discovers Hermione has knowledge of a powerful spell or magic item that could help them overthrow Voldemort. So, they save her to get that information. For example, she might know of a way to break a powerful curse that Voldemort has placed on them.