One possible consequence could be a change in his fighting style. Without his eye, he might have to rely more on his other senses like hearing and smell, similar to how blind ninja in the Naruto universe adapt. For example, he could focus more on using his chakra to sense the movements of his opponents.
Naruto might also go through an identity crisis. His whole life has been centered around being a ninja with chakra and using powerful jutsu. Losing his chakra could make him question who he is and what his purpose is. He would have to redefine himself and find a new way to contribute to the ninja world. This could be a long and difficult process for him.
Perhaps he was in a battle against a very strong enemy. The enemy might have used a special attack that specifically targeted his eyes, like a genjutsu that damaged his optic nerves when he broke free from it.
In this fanfiction, it could be that Naruto's left - eye loss is part of a curse placed on him by an ancient evil. This curse not only takes his eye but also starts to drain his chakra. Naruto then has to search for the origin of the curse to break it. Along the way, he meets some new characters who either help or hinder him. His relationship with Sasuke could also be affected as Sasuke might see Naruto as weakened and try to protect him in his own way, which Naruto would initially resist as he doesn't want to be seen as a liability.
Maybe he was protecting someone in Wave. He's always the self - sacrificing type, so he could have put himself in harm's way to save a villager or a friend.
Another reason might be related to a plot device in the fanfiction. The author could be using the loss of the mask to create a turning point in the story. It might lead to new relationships being formed or old ones being tested. For instance, his friends might react in different ways when they see his face without the mask, and this could drive the story in different directions.
One reason could be betrayal by his friends. For example, if someone he considered a close ally made a deal with his enemies behind his back, it would shatter his trust. Another might be lies from the village leaders he respected. If they hid important information or manipulated him for their own gains, Naruto would start to question who he could trust.
One interesting plot could be Naruto forgetting all his ninja skills. So he has to start from scratch, relearning basic jutsus. This would make for a great character development arc as he discovers his old abilities in new ways.
Naruto could become bitter. Losing trust, especially in those he once held dear, can make him view the world in a more negative light. He may no longer believe in the good of people so easily and might be more cynical. For example, he might not be as quick to offer help or friendship as he used to be.
Well, Naruto might rely on his other senses more. His sense of smell, which is already quite sharp, could be enhanced further. He could also use his chakra to sense the environment around him, like how he can detect the presence of others. And he'd probably train with his friends more, especially those like Hinata who can guide him using her Byakugan.