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.
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.
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 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.
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'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.
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.
Yes, there are likely to be such fanfictions. In the Naruto series, Sakura can be quite assertive and strong - willed. Her temper and skills could potentially be a source of intimidation for Naruto in the creative interpretations of fanfiction writers.
Naruto could have summoned Gamabunta. He has a strong bond with the toads, and in a moment of desperation, he might have called upon Gamabunta to break his fall or catch him on his back.
Perhaps in this fanfiction, Jiraiya discovers that Naruto is going to be the cause of a major catastrophe in the future. He might have seen a prophecy or some sort of sign that convinces him Naruto has to die to prevent this. It could also be that Jiraiya has been misled by false information about Naruto, which makes him think that Naruto has become an evil force that needs to be eliminated.