It could be about Naruto somehow getting the power of Ryuk. Maybe he finds the Death Note in his ninja world and has to deal with the moral implications of using it, like Light did in Death Note.
Ryuk is a Shinigami, and his stories would likely be centered around the themes related to death and the power of the Death Note. He may tell stories about how different people reacted when they first got hold of the Death Note. Some were greedy and tried to use it for personal gain, while others were more hesitant. He could also share stories about the Shinigami who have come before him and the unique situations they were involved in. Ryuk has a very different perspective from humans, so his stories would offer a strange and often disturbing view of the world, filled with moral dilemmas and the consequences of playing with the power of life and death.
Yes, there are some out there. You can start by looking on fanfic platforms like Archive of Our Own. Just search for 'Ryuk x Harry Potter' and you'll likely find a variety of stories with different takes on this unique crossover.
Common themes in Ryuk x Rem fanfiction include the discovery of new emotions. Since they are not exactly the emotional type in the original story, fanfiction writers like to explore how they would react to falling in love or developing a deep bond. Also, the theme of survival can come up. If they get involved in a situation where their lives as Shinigami are at risk, how they support each other through it can be a central theme in the stories.
The two main characters are Ryuk and Light. Ryuk is a Shinigami, a death god from the Shinigami realm. He drops the Death Note into the human world which Light Yagami finds. Light is a brilliant high - school student who becomes obsessed with using the Death Note to create a world free of crime by killing criminals.
In Death Note fanfiction, Ryuk and Rem have a rather complex relationship. Ryuk is more of an indifferent observer of the human world, while Rem has a deep emotional investment in Misa. Their interactions can be really interesting. Sometimes they might cross paths in the Shinigami realm or in relation to the actions of their respective human owners. Ryuk might find Rem's loyalty to Misa strange given his own non -chalant attitude towards Light. It's these differences that can create some really engaging scenarios in fanfiction.
The unique combination of two very different universes makes it special. Ryuk's otherworldly and somewhat amoral nature contrasted with Harry's heroic and moral character in the magical world is a big draw.