Two in the Shadow

Midaregumo is a movie starring Yûzô Kayama, Yôko Tsukasa, and Mitsuko Kusabue. A man falls in love with the widow of a man he killed in a car accident. Eventually she falls in love with him in return.
A man is involved in a fatal car accident, and though he is blameless, his company transfers him to a remote branch in a small town. Before he leaves, he gives the man's widow a large sum of money that she uses to move back to her hometown.