One reason could be loyalty. Emmett is part of the Cullen family, and Bella is important to Edward, who is also his family. So, he would do anything to protect her for the sake of family unity. Another reason might be his sense of justice. If he saw Bella in an unfair or life - threatening situation, his nature would drive him to save her.
Well, in many fanfics like this, Emmett might save Bella from a physical danger like an attack by other vampires. Maybe Edward was in a situation where he couldn't protect Bella, and Emmett's strength and bravery came into play. He could have fought off some rogues who were after Bella.
One characteristic is the exploration of complex relationships. For example, the love triangle between Bella, Edward, and Emmett can create a lot of emotional tension. Another is the development of unique character traits. In these fanfictions, Emmett might be shown as more sensitive or Edward as more conflicted than in the original works.
In these fanfictions, Emmett's dominance often shows in his protectiveness. He'll be very quick to step in front of Bella when there's danger. For example, if there's a threat from another vampire or some other supernatural force.
Well, Emmett's physical strength can also have an impact on Bella. In some stories, seeing Emmett's power makes Bella strive to become stronger herself. Maybe she starts training with him, and through this process, she not only becomes more physically capable but also gains more confidence. This new - found confidence then affects her relationships with other characters as well. Moreover, Emmett's jovial personality can bring out a lighter side of Bella. When she's around him, she might find herself laughing more and being less brooding, which is a big change from her usual self in the original story.
Friendship is a common theme. Many fanfics explore the idea of Bella and Emmett having a deep, platonic friendship that is different from her relationships with other Cullens.
One possible reason could be that Edward believes Charlie is a threat to Bella in some way that Charlie doesn't realize himself. Maybe Charlie unknowingly gets involved with some dangerous elements, and Edward, with his vampire senses, detects it.
Betrayal is a very common theme. Since Edward is cheating on Bella with Emmett, it's a form of betrayal of Bella's trust. Another theme could be jealousy. Bella would likely be jealous of Emmett, and there might be some envy from Emmett towards Bella as well. Also, there could be a theme of self - discovery. All the characters might go through a process of realizing who they are and what they really want in relationships after such a big upheaval.
One interesting fanfiction could be about an alternate universe where Bella has to choose between Edward and Jasper in a more complex situation involving Emmett as a mediator. In such a story, the dynamics between the characters can be explored in depth, with their different personalities and abilities coming into play.
The themes could include love triangles gone wrong. In the original 'Twilight' series, there is a love triangle between Bella, Edward, and Jacob. But this fanfiction takes it in a different direction with Bella, Edward, and Emmett. It also might touch on the theme of impulsiveness. Bella's actions of cheating can be seen as impulsive, breaking the established relationship with Edward.
In some fanfictions, they might be reimagined as siblings. However, in the original 'Twilight' series, they are not siblings. Fanfiction often takes creative liberties to explore different relationships between characters.