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.
A possible plot is that Hermione, while researching for a new spell theory, stumbles upon a long - forgotten charm that was created by Rodolphus. This draws her attention to him, and she decides to find out more. Meanwhile, Rodolphus, who has been in hiding, senses someone is looking into his past work. When they meet, there is a clash of personalities. However, as they start to discuss the charm and its potential, they find common ground. Another idea is that in a world where magic is fading, Hermione believes that Rodolphus might have some knowledge that could help. She approaches him despite the risks. He, in turn, sees an opportunity to make amends for his past deeds through helping her. Also, they could be brought together by a prophecy that only they can fulfill, which forces them to put aside their differences and work together.
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.
One plot idea could be that in an alternate universe, Rodolphus, after realizing the error of his ways in the wizarding war, tries to make amends by protecting Hermione from a new dark threat. This could lead to a begrudging partnership that slowly turns into an unexpected friendship or more.
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.
One plot idea could be that Hermione and Rodolphus travel back to the time when the Hogwarts founders were alive. Hermione could use her knowledge to try and influence the early magical laws and education system. Meanwhile, Rodolphus, being from a different era, would have a hard time adjusting and his dark magic - influenced mindset might create conflicts. For example, he might try to introduce some of the more extreme pure - blood ideologies which Hermione would vehemently oppose.
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.