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.
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.
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.
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.
Jiraiya would probably offer some words of wisdom. He has a lot of life experience, so he might tell Naruto that crying is not a sign of weakness but a way to let out pent - up emotions. For example, he could say something like 'Boy, those tears are like the rain that nourishes the seeds of your growth.'
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.
Perhaps Naruto has just lost a fight against a powerful enemy and is feeling defeated. His crying is a result of his frustration and self - doubt. Jiraiya, covering him, then begins to train Naruto more intensively to help him overcome his weaknesses. Or it could be that Naruto has witnessed something truly horrifying in the ninja world, like a massacre. Jiraiya's act of covering him is the start of him guiding Naruto to understand the darker aspects of their world and how to face them bravely.
The plot could be that Naruto is crying due to the pressure of being the Jinchuriki. Jiraiya comforts him by saying that his strength is not just in the Nine - Tails but in his own heart. He gives Naruto the fan as a reminder of their bond and that he'll always be there for him, even if not physically.
In this fanfiction scenario, the emotional depth would be significant. Naruto crying while Jiraiya covers him could signify a moment of breakdown for Naruto. It could be that he has failed at something important, like a mission, and Jiraiya's covering is his way of saying it's okay. It could also be related to Naruto's past traumas resurfacing. Jiraiya, being the experienced and caring mentor, offers his protection both physically and emotionally. This simple act can hold a lot of unspoken emotions between them, such as trust, love, and the hope that Jiraiya can make things better for Naruto.
Jiraiya might comfort Naruto by sharing his own experiences. He could tell Naruto about the times he faced difficulties and how he overcame them. For example, he might talk about his training with the toads and how he grew stronger through perseverance.