stray (v.)

c. 1300, straien, of animals, "wander away from an enclosure or herd," also figurative, of persons, "wander from the path of justice or rectitude," a shortening of Old French estraier "wander about, roam, drift, run loose," said of animals, especially a horse without a master, also of persons, perhaps literally "go about the streets," from estree "route, highway," from Late Latin via strata "paved road" (see street).

On another theory (reprinted in OED), the Old French word is from Vulgar Latin *estragare, a contraction of *estravagare, representing Latin extra vagari "to wander outside" (see extravagant). Related: Strayed; straying.

"domestic animal found wandering from its enclosure or proper place," early 13c., strai, a legal term, from Anglo-French stray, estray, noun use of Old French estraié "strayed, riderless," past-participle adjective from estraier "to roam, drift, run loose" (see stray (v.), and compare waif).

c. 1600, of animals; 19c. of persons and things, from stray (n.) and in part a shortening of astray.