Perhaps Bellatrix attacks Hermione's friends, like Ron or Ginny. This enrages Hermione so much that she taps into a deep, dark magic she didn't know she had within her. With this new power, she confronts Bellatrix and after an intense duel, Hermione is able to defeat and kill her. In fanfiction, it often explores the characters' untapped potential and this could be one way to show Hermione's strength.
One possible plot could be that Bellatrix captures Hermione and tries to torture her for information about Harry. But Hermione, using her wits and some new-found powerful magic she has been secretly studying, manages to turn the tables and kill Bellatrix in self - defense.
It could be that Bellatrix has a plan to destroy Hogwarts completely. Hermione, being the intelligent and brave witch she is, discovers this plan. She devises a strategy to stop Bellatrix. During their encounter, Hermione uses a combination of her intelligence, knowledge of spells, and the element of surprise to overpower Bellatrix and ultimately kill her to save Hogwarts.
Yes, there are likely fanfictions out there with such a plot. The 'Harry Potter' fandom is vast and diverse, and some fanfiction authors explore dark and alternate storylines. However, these often deviate from the original positive and heroic themes of the series.
One reason could be pure hatred. Bellatrix despises Muggle - borns, and Hermione being a very intelligent and powerful Muggle - born would be a prime target for her wrath. Another could be jealousy. Hermione's skills and knowledge might make Bellatrix feel inferior, leading her to lash out.
Luna Lovegood might be involved. She could provide some unique magical items or knowledge to Hermione that helps in the fight against Bellatrix. Also, Severus Snape could be a character in the fanfiction. His complex relationship with both the Order of the Phoenix and the Death Eaters could add an interesting layer to the story. Maybe he has some information that Hermione needs to defeat Bellatrix.
Perhaps Bellatrix kidnapped Hermione to use her as bait to lure Harry. Bellatrix has always been extremely loyal to Voldemort and might think that by having Hermione, she can draw Harry out into the open. Hermione, being the intelligent witch she is, could try to outwit Bellatrix while in captivity, maybe by finding a way to send messages to her friends or even by trying to escape on her own.
She could face legal issues in the wizarding world. Killing is not taken lightly, even if it's Death Eaters she's killing. There might be a trial to determine if her actions were justified. If the wizarding authorities are corrupt or influenced by the wrong people, she could even be wrongly convicted.
One possible plot could be that Hermione is somehow under the influence of a dark magic or a powerful dark wizard. This dark influence makes her see Dumbledore as a threat to her friends or the wizarding world in a twisted way, and she is compelled to kill him.
One possible aspect of Hermione and Bellatrix fanfiction could be the exploration of their opposing natures. Hermione is a studious, rule - following Gryffindor, while Bellatrix is a wild and chaotic Death Eater. Fanfiction might play with the idea of how they interact in different scenarios. For example, in a scenario where Hermione is captured by Bellatrix, their exchanges could be filled with tension and power plays. Hermione's intelligence could be pitted against Bellatrix's brute force and loyalty to Voldemort.
In Hermione and Bellatrix fanfiction, the power dynamic is often an interesting point. Bellatrix has a great deal of power as a Death Eater, but Hermione has her own kind of power in her knowledge and magic skills. Some fanfictions may show a battle of wills between them, where Hermione refuses to be intimidated by Bellatrix's threats. This can lead to some really intense and exciting storylines, like when Hermione stands up to Bellatrix in a duel - like situation in a magically - created arena within the fanfic's plot.
It could also be that the situation was extremely dire. For example, the troll was about to destroy something very important, like a magical artifact that could cause great harm if it fell into the wrong hands, and Hermione saw killing the troll as the only way to prevent that.
In some fanfictions, it could be related to a power struggle within the wizarding world. If Hermione was seen as a threat to Ginny's family or her own standing in the magical community, Ginny could be pushed to the edge. Also, if there was a rift in their friendship over ideological differences, like Hermione's more logical and rule - based approach clashing with Ginny's more impulsive and instinctive nature in a very extreme way, it might lead to such a tragic outcome.