In fanfiction, Jiraiya seeing Naruto as Hokage can be a very emotional moment. It could be a vision Jiraiya has in a story where he's still alive, or perhaps it's a memory in a story set after his death. This often shows Jiraiya's pride in Naruto and his belief in Naruto's potential to lead the village.
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 might also isolate himself in certain fanfic scenarios. He feels that no one can truly understand the depth of his grief. He spends time alone, reflecting on all the things Jiraiya taught him and the memories they shared, like their time training on that toad -infested island.
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.
His character may become more withdrawn at first. Losing Jiraiya, who was like a father figure to him, could make Naruto less open and more focused on his internal pain.
One possible scenario could be that Naruto leaves to train in isolation. He might feel that he needs to become stronger on his own without the guidance of Jiraiya, and so he sets off to find new ways to improve his skills.
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.