Yuri is a minor character in the On the Way to a Smile novella "Case of Yuffie".
Yuri is a childhood friend of Yuffie. During the events of the novella, his mother falls ill with the mysterious "Midgar illness", and Yuffie is blamed for bringing the disease from Midgar. Yuri helps her escape from confinement by Godo, and the two leave Wutai for a short time, but eventually return. During this time, Yuri tells Yuffie that his mother was injured even before she contracted the illness, and agrees to help her find a cure to help clear her name.
The two venture to the Materia Cave south of Wutai to look for a Materia to heal the disease, where mysterious black water bubbles up and overwhelms them. Yuri, now oozing a black substance from his mouth, is carried from the cave by Yuffie and Red XIII. Yuri then admits he considers himself the cause of the "Midgar illness", as he was present in Midgar when Meteor fell, seeking a Materia to cure his mother, and returned to Wutai before Yuffie did.
The three return to Wutai where those infected, including Yuri's mother, have been quarantined to prevent the disease from spreading. Over the next two years as Yuffie searches for a cure, Yuri's mother dies but he survives, and presumably lives long enough to be healed during or after the events of Advent Children.
"Yuri" is a common female Japanese name meaning "lily", and a common male Russian name "Юрий".