In such a fanfiction, perhaps the village's needs are always put first by Naruto, and his sister gets the short end of the stick. For example, he might not be there to protect her when she faces some bullies in the village just because he's too busy with village affairs. This could cause her to doubt Naruto's love for her, and she might even consider leaving the village in search of a place where she feels more valued.
It could be a jealous ninja in the village. This person might see Naruto's sister as an easy target since Naruto is often preoccupied. They could spread rumors about her or try to make her life difficult at the ninja academy, taking advantage of Naruto's absence.
One possibility could be an original character created specifically for the fanfiction. This gives the writer the freedom to shape her personality and backstory completely. Another could be a minor character from the Naruto series that doesn't get much attention, like Tenten's sister if she had one. It could also be a reimagined version of Hinata as Naruto's sister. Since Hinata has her own story in the original series, reimagining her as Naruto's sister with a neglected past could lead to some interesting fanfiction ideas.
He might try to prove himself. Naruto has always been a determined character. He could focus on his ninja training more intently, aiming to show everyone his worth despite being neglected. Maybe he'd also start to distance himself a bit from his family situation and form closer bonds with his friends like Sasuke and Sakura, who might understand and support him through this tough time.
She might feel guilty. Since they are siblings, she could be aware of Naruto's neglect and try to make it up to him in small ways, like sharing her food or secretly leaving him little gifts.
It's popular because it explores a different side of Naruto's story. The idea of him having a sister who cares when others don't adds an interesting dynamic. People like the concept of family loyalty and the sister being a support system that Naruto was lacking in the original story.
Well, it can add a lot of depth to the story. It could make Naruto more determined to prove himself. He might seek validation outside of his family, which could lead him to form stronger bonds with his friends like Sasuke and Sakura. This neglect could also be a driving force for him to become stronger, as he wants to show his family what they're missing out on.
Some themes might include perseverance. Despite the neglect from his sister, Naruto continues to move forward. There could also be a theme of forgiveness. Maybe at some point in the fanfiction, Naruto has to decide whether to forgive his sister for neglecting him. And family drama is definitely a common theme. It can explore the complex relationships within a family, especially in the context of the Naruto world.
Often, a common theme is the sister's feelings of isolation. Since she's neglected, she might feel all alone in the ninja world. She may not have many friends as people are more interested in Naruto. And also, there can be a theme of redemption or revenge. She might want to prove herself to those who neglected her, either by showing them how great she can be in a positive way (redemption for herself in their eyes) or by getting back at them in some way for the years of neglect (revenge, though this is less common in more positive fanfictions).
It could be a member of Naruto's family who is fueling the neglect. Maybe an older relative who believes that the sister has more potential or is more worthy of attention and resources. This person could actively try to keep Naruto down.