Well, in some fanfictions, he might obtain it through a strange encounter. Maybe he stumbles upon an ancient relic during a mission that contains the power of the broken eye dojutsu and it somehow bonds with him.
It might have the ability to see through illusions that normal eyes can't. Since it's a dojutsu, even if it's broken, it could still have some enhanced visual powers. For example, it could detect the tiniest movements of an enemy, giving Naruto an edge in combat.
The third eye might have the power of long - distance vision. Naruto could use it to spy on enemy camps or look for missing comrades from afar. This would be a useful addition to his skills, especially when planning strategies or rescuing hostages. He could also use it to keep an eye on the Akatsuki's movements across different regions without having to be physically close.
If Naruto had a third eye in fanfiction, it could greatly enhance his perception abilities. He might be able to detect hidden enemies or traps more easily. For example, in battles, he could see chakra movements from all directions without having to rely so much on his regular senses. This could make him even more formidable in combat and change the dynamics of his fights against powerful foes like Sasuke or Pain.
It could be due to a battle injury. Maybe he got into a really tough fight with a powerful enemy, and in the process, lost an eye. For instance, a fight against a rogue Akatsuki member who has a very dangerous eye - related jutsu.
This change in Naruto having one eye could lead to a whole new character arc. Maybe he'd be more self - conscious about his appearance, which could affect his relationships. He might also develop new jutsu that are more suitable for his one - eyed state, like a jutsu that uses his remaining eye's chakra in a more focused way.
In some fanfictions, Naruto's eye bloodline is linked to a long - lost clan. His eyes hold the key to unlocking ancient secrets and powers. This often leads to him going on a quest to find out more about his heritage and the true nature of his eyes. For example, he might discover that his eyes can open portals to other dimensions which is a really cool concept.
One possible plot development could be Naruto using the flowing eye to discover new jutsu. For example, he might be able to see the chakra flow in a different way and create unique attacks. Another could be that the flowing eye attracts the attention of new enemies who want to either steal it or destroy it because they fear its power.
There's also the possibility that it's an accidental injury caused by one of Naruto's friends during a training session gone wrong. For example, Sasuke could accidentally unleash a jutsu that hits Naruto's eye while they are sparring.
One consequence could be that Naruto becomes more isolated. He may feel like he's a burden or that he's not as strong as he used to be. However, this could also lead to him becoming more determined to overcome his disability. He might train harder to develop his other senses, like his hearing and sense of smell, to make up for the loss of his eye. This could ultimately make him a more well - rounded and unpredictable fighter.