In some fanfictions, a scenario could be that Naruto discovers a hidden side of the Kyuubi. Maybe there are memories or emotions that the Kyuubi has been suppressing. Naruto helps the Kyuubi deal with these, and this act of kindness makes the Kyuubi warm up to him. They then start to build a friendship based on trust and mutual support.
A common scenario is when Naruto is on the verge of death. The Kyuubi realizes that if Naruto dies, it might also be in a bad situation. So, it decides to cooperate and in the process, they start to understand each other better and become friends. Another is when Naruto enters the Kyuubi's lair in his mindscape and instead of fighting, he tries to have a peaceful conversation, which leads to friendship.
One common scenario is that they get trapped in a different dimension together. In this strange new place, they have to rely on each other to survive. Without the distractions of their normal lives and the expectations of the village, they really get to know each other on a deeper level and become best friends.
In some fanfictions, Naruto might start by trying to understand the Kyuubi's pain. He could use his own experiences of being an outcast in the village to empathize. As he shows this understanding, the Kyuubi begins to see him as different from the other humans who just fear it. They might start having conversations in Naruto's mindscape, gradually building a bond of mutual respect.
One common scenario is during a mission. Naruto might be paired with a new character in a team for a mission. Through facing challenges together, they develop mutual respect and friendship. They learn to rely on each other's skills, like Naruto's strength and the other character's unique abilities.
The Fem Kyuubi might be in trouble or weakened somehow. Naruto senses this and instead of taking advantage, he offers his help. He uses his own chakra to soothe her or protect her from whatever is threatening her. This act of kindness surprises the Fem Kyuubi. She has never experienced such a selfless act from a human before. This makes her lower her guard and start to trust Naruto. They then start to interact more often, with Naruto bringing her stories from the outside world and the Fem Kyuubi sharing her ancient knowledge with him, thus forming a friendship.
One interesting scenario could be Naruto learning to control the Kyuubi's power in a unique way that wasn't shown in the original series. For example, he might use it to create new jutsu that combine his own skills with the Kyuubi's raw power.
Well, it often involves imagining unique powers and circumstances. Maybe a special ritual or a rare encounter could trigger the transformation.
In this fanfiction, perhaps the fem Kyuubi protects Naruto by leading him to hidden places in the forest that are safe from the reach of his foes. She might use her knowledge of the area, which she has gained over the years of being in the Naruto world, to find these secret spots. And along the way, she could also teach Naruto some new skills or give him insights about his own powers that he hadn't considered before.
Well, in this type of fanfiction, perhaps Naruto in the Kyuubi's place would gain a deeper understanding of the Kyuubi's power and its origin. He could also communicate with the other tailed beasts in a different way. As for the Kyuubi in Naruto's place, it might have to face Naruto's emotional struggles, like his longing for acceptance from the village. This could lead to some unexpected character development for both Naruto and the Kyuubi.
A common theme is redemption. Kyuubi, through its obsession with Naruto, might find a path to redemption. Since Naruto represents all that is good in the world of 'Naruto', Kyuubi could be influenced to change its ways. For example, it could start to care about the village and the people in it, which is a huge change from its initial malevolent nature.
One interesting scenario is when Naruto enters a special mental realm created by the Kyuubi for training. In this realm, time may pass differently, allowing him to train for a long time while only a short time passes in the real world. Another scenario could be that the Kyuubi actually teaches Naruto some ancient and forgotten ninja techniques that were lost over time but were known to the powerful beasts like itself.