It's hard to say exactly. Maybe there was a hidden plot twist or a secret they discovered that made them run. Maybe they were trying to avoid being caught by some villains. Without more details from the visual novel, it's tough to be certain.
One challenge could be acceptance. Since Ichigo is from the human world and a Shinigami, and Nemu is an Arrancar, their union might not be easily accepted by either the Soul Society or the Arrancar community. Another challenge could be communication. They come from different backgrounds and cultures, so understanding each other's values and ways of thinking might be difficult at times.
One great 'Naruto Kurotsuchi' fanfic is 'The Hidden Strength of Kurotsuchi'. It delves into her character development and how she overcomes various challenges in the Naruto universe. It's really engaging as it shows her unique abilities and her relationships with other characters in a new light.
A possible fanfiction idea could be that Naruto and Kurotsuchi become friends during a diplomatic mission between their villages. Naruto, being the ambassador of sorts from Konoha, and Kurotsuchi representing Iwagakure. They start off with some misunderstandings, but as they talk more, they realize they have common goals, such as improving the relations between their villages for the greater good of the ninja world.
Definitely not. The Naruto franchise promotes positive themes such as self - improvement and camaraderie. A fanfiction with the concept of slavery related to a character is not in line with the overall tone and message of the Naruto series. It may also be offensive to many fans who enjoy the original story for its positive and inspiring elements.
One idea could be that Naruto gets lost in Iwagakure's territory during a mission. Kurotsuchi finds him. At first, she's suspicious of him, but Naruto's friendly nature wins her over. As they try to find a way for Naruto to get back to Konoha, they have to rely on each other. This mutual dependence could lead to the start of their love story.
The plot could involve Nemu saving Ichigo's life during a fierce battle. This act makes Ichigo see Nemu in a new light. They begin to spend more time together, sharing their past traumas and dreams. As they fall deeper in love, they decide to get married. However, they have to keep it a secret at first due to the political situation between Hueco Mundo and Soul Society. Eventually, their love story becomes an inspiration for others in both worlds.
There are definitely some out there. I remember reading one where Deidara and Kurotsuchi were forced to team up against a common enemy. During this time, they got to know each other better than they ever had before. The story was really well - written, with great descriptions of their characters and how they interacted. It was a slow - burn kind of story, which made it even more interesting as their relationship developed over time.
Another theme is her relationships. This can be her relationships with her fellow villagers, like her comrades in the village, or her relationships with characters from other villages. For example, some fanfictions explore her interactions with Naruto and his friends when they visit the Hidden Stone Village.