One possible plot could be that Hermione is on a mission to gather information from Rodolphus. Maybe she suspects he has some knowledge about the remaining Death Eaters or some dark magic secrets that could help in the post - war rebuilding of the wizarding world.
I'm not sure of specific 'Hermione tracks down Rodolphus' fanfictions off the top of my head. You could try searching on fanfiction - specific websites like Archive of Our Own or FanFiction.net. Just type in the keywords 'Hermione tracks down Rodolphus' in their search bars, and you might find some interesting stories.
One possible plot could be that Hermione is on a mission to bring Dolohov to justice for his crimes during the wizarding war. She uses her intelligence and magic skills to follow his trail.
One difficulty could be that it's a relatively niche plot. Not all fanfiction writers might be interested in exploring this particular scenario of Hermione tracking down Rabastan, so there may be fewer works available. Another issue is that if the fanfiction is not tagged correctly on the platforms, it can be really hard to find using the search function.
I'm not sure of specific 'hermione tracks down dolohov' fanfiction off the top of my head. You could try searching on major fanfiction platforms like Archive of Our Own. There might be some interesting stories there.
Finding that particular fanfiction might be a bit of a challenge. Some smaller, more niche fanfiction communities or forums dedicated to the relevant fandom (presumably Harry Potter) might also have it. You could also try reaching out to other fans in the community through social media platforms like Twitter or Tumblr, asking if they know of any such fanfics. Just make sure to follow the rules and etiquette of each platform.
She would likely be on high alert. Hermione is a smart witch, so she would quickly assess the situation. She might immediately reach for her wand and prepare to defend herself. Her first reaction would probably be fear, but she would soon overcome it with her determination to not be a victim.
One good one might be 'Rodolphus' Redemption' where Rodolphus starts to question his Death Eater ways after meeting Hermione. It shows a different side of him and how their interactions could lead to a change in the wizarding world's power dynamics.
Hermione's leadership skills might also play a part. If she takes charge in a group or a mission, and is able to guide others effectively towards a common goal. Rodolphus, seeing her lead with confidence and intelligence, would surely be impressed.
Maybe he is attracted to Hermione's character traits like her intelligence and courage. Fanfictions often explore different aspects of her personality in unique ways that might intrigue him.