subs. phr. (common).A state of feigned yet very vigilant indifference to ones surroundings. [Foxes were supposed to sleep with one eye open.]
1830. J. BARRINGTON, Personal Sketches of His Own Times, vol. III., p. 172 (ed. 1832). Mr. Fitzgerald he supposed was in a FOXS SLEEP, and his bravo in another,who, instead of receding at all, on the contrary squeezed the attorney closer and closer.