There are several visual novels where Rin could potentially die, but one common one is 'Fate/Stay Night'. It depends on the specific route and choices made by the player.
It can change the dynamics of relationships. For instance, it might create a new friendship or rivalry among characters. If Rin is in love with Naruto, Sakura might feel threatened as she also has feelings for Naruto. So, it can stir up emotions among the female characters.
Another possibility in fanfiction is that Naruto succumbs to a deadly disease or poison. It could be a new, mysterious illness that the medical ninjas in the village can't cure in time, leading to his death.
Well, as of now, Naruto is still alive in the Boruto manga. There might be some intense battles and challenges, but no death for him yet. Maybe you got some wrong information?
There could be a scenario where Naruto sacrifices himself to save Boruto or the entire Hidden Leaf Village from a catastrophic event like a massive attack by an unknown and dangerous force. He might use all his chakra to protect the village, leaving him with no energy to survive.
Fanfiction often explores their relationship in different ways. For instance, it might show how Naruto's ideals could have influenced Obito's decisions if they had interacted more. Naruto's belief in friendship and never giving up could have made Obito think twice about his actions.