One common theme is redemption. The heroine has to prove her innocence and in the process, she redeems herself in the eyes of the hero and the society in the story. For example, she might have to face a lot of social ostracism because of the false accusations, but through her actions and the truth coming out, she regains her standing.
Love in the face of adversity is another theme. Despite the false accusations, the heroine often finds love. It could be with a man who initially doubts her but then comes to believe in her innocence. This kind of love story set against the historical context is very appealing. In many such novels, the historical period also plays a role. The social norms and power structures of the time can either be part of the problem causing the false accusations or part of the solution in helping the heroine clear her name. For instance, if it's a time when women had few rights, it makes her fight for justice even more difficult but also more heroic.
One such novel could be 'The Forbidden Love of a Wronged Lady'. In this story, the heroine is wrongly accused of a crime she didn't commit. It weaves a tale of love and intrigue against a historical backdrop.
One such novel could be 'The Viscount's Vixen' where the heroine is wrongly accused of stealing a precious heirloom, but in the end, love prevails. It has an interesting plot where the hero initially believes the false accusations but then realizes the truth.
Since I don't have access to this particular fanfic, it's hard to give a detailed account. However, generally speaking, in a fanfic where a character like Buck from '911' is falsely accused, it often serves to create drama and tension. The story might explore how Buck deals with the false accusations, how it affects his mental state, his friendships, and his standing in the community or among his colleagues. It could also be a vehicle for exploring themes of justice, truth, and redemption as Buck tries to clear his name.
In many such fanfictions, Naruto is initially hurt by the false accusations, especially if they come from his friends or the people he trusts in the village. But then, his strong will kicks in. He starts to analyze the situation carefully. He may talk to people who are neutral or try to find contradictions in the false accusations. He uses his ninja skills not just in combat but also in detective - like investigations to clear his name.
One example could be a fanfiction where Naruto is wrongly accused of stealing a powerful jutsu. In the story, perhaps a rival village's ninja frames him by planting false evidence at the scene. Another could be a situation where he is falsely accused of being a spy within his own village due to some misunderstandings and false testimonies.
There was a novel called " The Inheritor ". The protagonist was originally a poor young man, but in an accident, he inherited an inheritance. However, he found that the inheritance was wrongly given to another person, so the protagonist embarked on a journey of exploration about justice and wealth.
You could try searching on popular fanfic websites such as Archive of Our Own (AO3). It has a large collection of fanfictions from various fandoms, including '911'. Just type in relevant keywords like '911 Buck falsely accused' in the search bar and see if any results come up.