One common element could be a distorted view of the characters' personalities. For example, Naruto might be portrayed as more erratic or self - destructive. Another might be a darker, more hopeless world - building compared to the original Naruto universe.
In some fanfictions, Naruto might be depicted as mentally unstable for various reasons. One could be the extreme stress he endures. He has lost many people in his life, like his parents at a young age. This could potentially lead to psychological trauma that some fanfic authors might explore and exaggerate, making him seem mentally unstable.
It adds more depth to the genre. By showing Naruto as mentally unstable, it allows for different types of stories. For example, stories about his recovery or his struggle with his mental state can be created, which makes the fanfiction more diverse.
I'm not really into promoting fanfics that involve mentally unstable themes as they can often be quite dark and disturbing. However, you can try searching on some major fanfic platforms like FanFiction.net or Archive of Our Own and use the relevant tags to look for such works, but be cautious as they might not be suitable for all readers.
One possible reason could be the extreme pressure he faces in the fanfic. Maybe he has to deal with much more powerful enemies alone, which overwhelms his mental state. Also, if he experiences a lot of betrayals in the fanfic, like friends turning against him, it could lead to his mental instability.
Bind the Nation's Fate: Me! Mental illness! Teammate Sister Bao 'er "is for you. The story revolved around a strange game. The protagonist, Wu Tian, had transmigrated to a parallel world and was bound by the system to have a mental illness. He and a little loli became teammates on the national team. The countries mocked them for not having any hope for them, but when they entered the game and faced various situations, they showed their superior strength. I hope you like my recommendation. Muah ~
The fem Kyuubi could be initially attracted to Naruto's struggle with the Kyuubi inside him. She decides to help him. As Naruto's mental state improves due to her efforts, they could develop a romantic relationship. For example, she could teach him how to better control the Kyuubi's chakra, and in the process, they fall in love.
Maybe Naruto's mental instability is a result of suppressing the Kyuubi for so long. The fem Kyuubi fanfic could explore how she tries to break through his mental barriers. She could use her own unique connection to the Kyuubi's power to reach Naruto on a subconscious level. This could lead to a series of adventures where Naruto has to face his inner demons with her help.
Often, you'll find themes related to the stigma around mental illness in the wizarding world. In these fanfictions, characters with mental instability might be ostracized or misunderstood. For example, if a character shows signs of depression after a dark wizard attack, they might be seen as weak rather than getting proper support. Another theme could be the exploration of how different magical creatures or artifacts could either cause or help with mental instability. For instance, a cursed object might slowly drive a character mad, while a magical plant could potentially have healing properties for a troubled mind.