Waif itself is a stray, if we consider its first meaning the home from which it came. Tracing back to an Anglo-French adjective waif meaning "stray, unclaimed," the English noun waif referred in its earliest 14th century uses to unclaimed found items, such as those gone astray (think cattle) and those washed ashore (think jetsam), as well as to the king's (or lord's) right to such property. Stolen goods abandoned by a thief in flight eventually came to be referred to as waifs as well, as later did anything found without an owner and especially by chance. (It's interesting to note that the verb waive, used in modern English in phrases like "waive a fee" or "waive one's rights" comes from the same Anglo-French source as waif and was at one time used to mean "to throw away (stolen goods).") The emphasis on being found faded as waif came to be applied to any stray animal or person, and especially to a homeless child, and in the late 20th century the current most common meaning of "an extremely thin and usually young woman" developed.