Kurama might become angry at first. He's a powerful being and being neglected would likely wound his pride. He could start causing some minor disruptions inside Naruto, like making it harder for Naruto to access his chakra.
They could become resentful. They might start to avoid Naruto altogether and refuse any summons. They could also start to act out in the forest, scaring away other animals or causing minor disruptions just to show their displeasure.
Perhaps he's been influenced by someone who gives him bad advice. For example, if someone tells him that natural talent is enough and training is overrated. Also, he could be dealing with some personal problems, like a conflict within his family or among his friends that takes up all his time and mental energy, causing him to neglect training.
He might start to rely on his friends more. For example, Sasuke and Sakura could become his main source of emotional support. He would focus on training with them and sharing his feelings, which in turn helps him to grow stronger and more independent.
One great 'Female Naruto Shikamaru AU' fanfiction is 'The New Path'. In this story, the female Naruto has a completely different dynamic with Shikamaru. It explores how their relationship might develop in an alternate universe where Naruto is female. The characterizations are really well - done, staying true to the original personalities while also adding new twists due to the gender change.
Another reason is that it allows for exploration of the darker side of the Naruto universe. The neglect of Naruto can be used as a starting point to show the flaws in the village system and how it can wrong an innocent child. It adds depth to the overall Naruto story and world - building, which fans find interesting.
The reason for 'Naruto ANBU Neglected' fanfictions is that the ANBU have a lot of potential for interesting stories. In the Naruto world, they are sort of in the background. Writers are drawn to them to show what their lives are really like, the things they face that others in the village don't understand. They might be neglected in the main story, but in fanfiction, they can be the focus. For example, their loyalty to the village despite being overlooked is a great theme to explore.
In a fanfiction, perhaps neglected Naruto runs away from Konoha and ends up in the same area as Yugito. Yugito, having also faced her own share of hardships, takes Naruto under her wing. They bond over their experiences, and Yugito helps Naruto to better understand his chakra nature by sharing her knowledge of the tailed beasts' chakra. This could lead to Naruto developing new abilities and a newfound confidence.
It could also be to add more depth to their relationship. When they are neglected, they have to rely on each other more. For example, in a fanfiction where the village turns their backs on them, Naruto and Sasuke might form an even stronger bond as they face this together. This gives writers a chance to develop their friendship in new and interesting ways. Also, it can be a way to introduce new plotlines and conflicts that wouldn't exist in the original story. By changing their status from being in the center of attention to being neglected, new challenges and opportunities for character growth are created.