Unwritten books is a reference to a large and potentially infinite body of literature that has not been written, but has been somewhat referenced. Typically, an “unwritten novel” is referenced as an idea to be implemented in the future. Many such unwritten novels never see the light of day.
Although the term mentions books specifically, “unwritten books” can be used to mean any literary work, including poems and short stories. The concept encompasses works that will never be written, as well as works that might end up being written in the future.
Unwritten stories obviously have no authors, however they can have authorship claims cast upon them. If an author says that she intends to write a novel, this unwritten novel will now have an authorship claim by her.
An unwritten work might spark an authorship war, when multiple authors claim an intention to create the story. The war is won by a person who actually writes the work first.