Yes, a short story titled A Slice of Bread exists. It was written by a Romanian author Francisc Munteanu. The original title is O bucată de pâine. In Japan, it is known as 一切れのパン (Hitokire no Pan).
The story is about the escape of a Romanian who was captured by German troops during World War 2. During the escape, he met a Jewish rabbi who gave something wrapped in a handkerchief. The rabbi said that it contained a slice of bread and only to open it if it is really needed. [...] (spoiler ahead about the ending)
After a long hardship and without opening the handkerchief, the escapee reached home. When his wife asked what the handkerchief was, he answered with "a slice of bread", but when he opened it, a piece of wood fell instead of a slice of bread.
For info in English, looks like the same short story was published in Meanjin Quarterly, v.25, no.3, 1966, p.297-305, but apart from that, the detail in English is lacking. Though, it is kind of popular in Japan due to it being included in the Japanese (national) language textbook for middle-schooler.
- The full story in Japanese can be read in this blog.
- The abridged version in Japanese can be read in this blog.
- The English publication can be accessed/bought from Informit.