No, it's not common in the context of the real story. Characters exist within their own world in Yuri on Ice and don't typically engage with fanfiction which is something created by fans in our world.
It could be quite an interesting experience. They might be surprised at the different interpretations of their relationships and stories. For example, Viktor might be amused by how some fanfictions exaggerate his charm. Yuri could be either flattered or a bit embarrassed by how his insecurities are explored in some fictions.
Characters' reactions to watching Yuri on Ice fanfiction can vary greatly. Some might be critical, thinking that the fanfiction doesn't accurately represent them or the story. Others could be more open - minded and enjoy the creativity. They may find it a new way to look at their world. It could also potentially influence how they see themselves and their relationships with other characters in the long run. For instance, if a character in the fanfiction is portrayed as more confident, it might inspire the real character to strive for more confidence in their own skating and personal life.
It could lead to some self - awareness. Yuri might become more confident if he reads fanfictions that focus on his growth. Viktor could get new ideas for his coaching. Overall, it might strengthen their relationships as they see how fans view their bond.
There could be a fanfiction where Yuri is kidnapped for ransom. The kidnappers target him because of his fame and the wealth associated with his skating career. His family and friends are distraught but soon gather resources and work with the police to try and rescue him. They face many challenges along the way, like deciphering the kidnappers' demands and finding their hideout.
One common theme is friendship. Female characters often form deep and meaningful friendships with Yuri. For example, they might support each other through tough skating competitions. Another theme is self - discovery. Yuri may learn more about herself through her interactions with female characters.