At first, Naruto might isolate himself. He doesn't want to be around others as he is so consumed by his grief. He just sits in his room or goes to a quiet place where he can cry alone and think about Jiraiya.
Over time, Naruto shares his feelings with his friends. He realizes that he can't carry this grief all by himself. His friends support him, and through their love and understanding, Naruto slowly starts to heal. But he never forgets Jiraiya, and his memories of him always stay with him, even as he moves forward.
One possible reason could be that Naruto is feeling lonely. Despite having friends, he still has moments when the weight of his past, like being an orphan and ostracized in the village as a child, hits him hard. Jiraiya might see Naruto crying because of these memories resurfacing.
In fanfiction, Jiraiya's death can also be used to explore themes of sacrifice. He sacrificed himself for the greater good, and this can be further elaborated in different stories. For example, some fanfictions might show how his death inspired other characters to be more selfless.
Naruto is devastated. He feels a huge void in his heart. Jiraiya was the one who believed in him from the start, and his death makes Naruto question a lot of things. He might even start to doubt his own strength for a while.
Jiraiya's comfort gives Naruto the confidence to face his fears. For example, if Naruto was crying because he was afraid of a powerful enemy, Jiraiya's words of wisdom and support would make him more determined to train harder and find a way to defeat that enemy in the future.
One possible fanfiction could be that Naruto is crying after a particularly tough mission where he lost a comrade. Jiraiya finds him and offers his fan, which has a special significance. He tells Naruto about his own losses and how he overcame them, inspiring Naruto to keep going.
Sometimes Naruto copes by throwing himself into his training. He uses the pain of losing Jiraiya as fuel to become stronger.
One scenario could be that Jiraiya is poisoned before his fight with Pain. In the fanfiction, an enemy within the village who is secretly working for Pain's forces might have poisoned his food or drink. So, when he goes to face Pain, he is already weakened, and this ultimately leads to his death. Another possibility is that Jiraiya's death is a result of a time - traveling plot. If there is time - travel involved in the fanfiction, his actions in the past might accidentally create a situation where he has to die to preserve the timeline.
He might become more determined. Losing Jiraiya was a huge blow, but it could fuel his desire to become stronger and protect the village even more.
Kakashi could step up more as a mentor. He already has a connection with Naruto and could help him develop his skills further.
It could be that Naruto has lost a dear friend. He is overwhelmed with grief. Jiraiya comes to his side. He doesn't say much at first but just gives Naruto a big hug. Then he starts to talk about the impermanence of life and how those who are gone would want Naruto to keep moving forward and be strong for their sake.