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.
A possible plot development is that Naruto has made a big mistake that has put the village at risk. He's crying out of guilt and fear of the consequences. Jiraiya covers him and offers his support, but also tells Naruto that he has to face the situation and make amends. Another idea is that Naruto has a premonition of Jiraiya's death. His crying is out of the fear of losing his mentor. Jiraiya, covering him, tries to console Naruto and at the same time, prepares him for the future without his presence.
One possible plot development could be that Naruto's fear is related to a new and powerful enemy in the Hidden Leaf Village. Jiraiya, covering for him, might train Naruto in secret to help him overcome his fear and face this threat. For example, Jiraiya could take Naruto to a secluded place and teach him new jutsu.
One possible plot development could be that Jiraiya discovers the source of Naruto's fear is related to a new and powerful enemy. He then decides to train Naruto more intensively to face this threat. For example, he might teach Naruto a new jutsu that can be used against this feared adversary.
Jiraiya is also a confidant. Naruto can trust him with his fear, and Jiraiya can keep Naruto's secrets. This relationship allows for a deeper bond between them, which could lead to Naruto opening up more about his feelings and Jiraiya being able to provide more targeted help.
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.
He also acts as a mentor. Jiraiya has a wealth of knowledge and experience. In this situation, he can use his wisdom to help Naruto understand and deal with his fear. He might tell Naruto stories of his own times of fear and how he coped, which can inspire Naruto.
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 plot development could be that Naruto quickly masters basic chakra control under Jiraiya's strict training. This early success might make Naruto overconfident, leading to a challenge where he realizes he still has a lot to learn. For example, he might face a powerful opponent in a sparring match arranged by Jiraiya and struggle initially, teaching him the importance of continuous training.
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 a fanfiction where Naruto is sealed away, there could be a focus on the emotional turmoil of his friends and family. Hinata, for example, might be extremely distraught and use her Byakugan in new ways to try and find Naruto. Sasuke could also return to the Leaf Village out of loyalty to Naruto and join the efforts to unseal him. The story could also explore how the younger generation of ninjas, inspired by Naruto's legacy, strive to become stronger to free him.
One possible plot development could be that Naruto gains a whole new level of power and is able to see and understand the world in a different way. He might be able to use the Rinnegan's abilities to finally bring true peace to the ninja world. For example, he could use the power of the Rinnegan to better understand the motives of his enemies and find non - violent solutions to conflicts.