Waif comes from Old Northern French gaif, which was probably from a Scandinavian root meaning ‘something loose or wandering’. In medieval English it was a legal term used in the phrase waif and stray to refer to an unclaimed item of property or a stray animal. By the late 18th century waif had assumed its modern meaning. The verb waive is related to waif: it comes from Old French gaiver ‘allow to become a waif, abandon’, and was originally a legal term.