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.
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.
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.
The characters of Bella and Emmett are central. Their personalities need to be maintained while exploring a new relationship in the fanfic. The 'lemon' elements often add a layer of passion. Also, the plot has to be engaging, perhaps involving some sort of conflict or challenge that their relationship has to overcome, which is different from the original storylines in the related series.
Since 'lemon' fanfics are inappropriate, we can talk about common themes in regular Bella and Emmett fanfics. One common theme is friendship. They are part of the same 'family' in the Twilight world, so stories might explore how they form a strong bond as friends. Another theme could be protection. Emmett being a strong vampire might be shown protecting Bella in various situations.
One common theme is unrequited love. Often, Emmett's love for Bella might not be fully reciprocated in the beginning, creating a sense of longing and tension.
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.
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.
Their relationship can be shown as a very protective one. Emmett, being the stronger one, might always be ready to shield Bella from any harm. For instance, if there are other characters who pose a threat, Emmett would step in front of Bella without hesitation.