A dog-eared piece is a term used to describe a book or document that has been worn down due to frequent use. The corners of the pages have been bent and folded, giving the appearance of a dog's ear. This is usually caused by the frequent handling of the book or document, such as when it is read or referenced often. The crossword solution for this term is 'CORNER, ' which accurately describes the physical characteristics of a dog-eared piece.