c.1200, aslepe, o slæpe, from Old English on slæpe (see sleep). The parallel form on sleep continued until c.1550. Of limbs, "numb through stoppage of circulation," from late 14c. Meaning "inattentive, off guard" is from mid-14c.
asleep a·sleep (ə-slēp')
adj.
In a state of sleep; sleeping.
Numb, as of a limb.
Dead.
In or into a state of sleep.
In or into a state of apathy or indifference.
Into the sleep of the dead.