Perhaps He Is (2005)

Original title: そうかもしれない

A non-prolific writer, Takayama Osamu and his wife, Yoshiko, though not blessed with children, live happily together. They should have had peaceful twilight years, but instead, Yoshiko suffers from Alzheimer's Disease, and Osamu also falls ill. Yoshiko, who cannot cope with daily life any longer, goes into a care home, and Osamu is admitted to a hospital, resulting in them living their remaining lives separately. One day, after some time, the couple who have kept battling their illnesses, manage to meet each other. Osamu breathes his last breath on the following day. People around Yoshiko find it difficult to inform her, but she seems to sense Osamu's death.