There could be some unexpected help. Maybe a hidden ally, like a hermit who lives in the forest and has been secretly watching Naruto all along, steps in and uses their special skills or knowledge to heal Naruto. This hermit might have some ancient healing techniques that save Naruto's life.
He might survive through his own sheer willpower. Naruto has always been a tenacious character. So, even when left for dead, his determination to live and achieve his dreams could keep him alive against all odds.
He could survive through his own tenacity and willpower. Naruto has always been a fighter, so even when left alone, he might find the inner strength to keep going. Maybe he discovers some hidden power within himself that he didn't know before.
Perhaps there was some sort of dark influence or mind - control at play. An enemy might have manipulated Kakashi's mind in such a way that he believed Naruto was a threat and thus left him for dead, not realizing his true self.
Maybe it's because of the deep bond they share and the sense of loss Kakashi feels when Naruto leaves.
Eventually, Naruto could grow resentful. If the ignoring persists for a long time, he might start to think that Kakashi doesn't care about him at all. This could change Naruto's attitude towards Kakashi and might even make him more rebellious in his training or actions. However, deep down, he still probably hopes for Kakashi's recognition and approval.
Naruto would be devastated. He sees Kakashi as a mentor and father figure. He might initially go into denial, not believing that Kakashi would actually abandon him.
In fanfiction, Kakashi might comfort Naruto by simply being there for him. Just sitting in silence, showing Naruto he's not alone. For example, they could be on the Hokage Rock and Kakashi would put a hand on Naruto's shoulder as they look over the village. It's a silent yet powerful form of comfort.
In this fanfiction, Kakashi could help Naruto in his training through mental conditioning as well. Naruto is often impulsive, so Kakashi may work on his patience and decision - making skills. He could use his Sharingan (if applicable in the fanfiction) to analyze Naruto's movements during training and give him detailed feedback. Moreover, Kakashi could introduce Naruto to different types of enemies and battle scenarios in a controlled training environment, which would broaden Naruto's understanding of combat and make him a more versatile ninja.
Well, it could strain their relationship. Avoidance usually creates distance, and in this case, Kakashi might feel hurt or confused as to why Naruto is avoiding him.
Their relationship is like a mentor - mentee bond. Kakashi has trained Naruto, and when he sees Naruto achieve great things, it can be overwhelming. For example, when Naruto masters a new jutsu that Kakashi thought was difficult for him, Kakashi might cry out of joy for Naruto's accomplishment.
It could become strained. Naruto snapping at Kakashi would create an initial rift between them. Kakashi might be taken aback by Naruto's outburst and Naruto, after snapping, might feel a bit guilty but also stubborn about his feelings, which would make the relationship tense for a while.