The Collaborative International Dictionary of English v.0.48:

Asleep \A*sleep"\, a. & adv. [Pref. a- + sleep.]
   1. In a state of sleep; in sleep; dormant.
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            Fast asleep the giant lay supine.     --Dryden.
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            By whispering winds soon lulled asleep. --Milton.
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   2. In the sleep of the grave; dead.
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            Concerning them which are asleep . . . sorrow not,
            even as others which have no hope.    --1 Thess. iv.
                                                  13.
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   3. Numbed, and, usually, tingling. --Udall.
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            Leaning long upon any part maketh it numb, and, as
            we call it, asleep.                   --Bacon.
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WordNet (r) 3.0 (2006):

asleep
    adv 1: into a sleeping state; "he fell asleep"
    2: in the sleep of death
    adj 1: in a state of sleep; "were all asleep when the phone
           rang"; "fell asleep at the wheel" [ant: awake(p)]
    2: lacking sensation; "my foot is asleep"; "numb with cold"
       [syn: asleep(p), benumbed, numb]
    3: dead; "he is deceased"; "our dear departed friend" [syn:
       asleep(p), at peace(p), at rest(p), deceased,
       departed, gone]

Moby Thesaurus II by Grady Ward, 1.0:

141 Moby Thesaurus words for "asleep":
   a stranger to, anesthetized, asleep in Jesus, at rest, benumbed,
   bereft of life, blind to, breathless, called home, callous,
   carrion, cataleptic, catatonic, caught napping, cold, comatose,
   croaked, dead, dead and gone, dead asleep, dead to, deadened,
   deaf to, death-struck, deceased, deep asleep, defunct, demised,
   departed, departed this life, destitute of life, done for, doped,
   dormant, drugged, dull, exanimate, fallen, fast asleep, finished,
   flaked-out, food for worms, gone, gone to glory, gone west,
   goofing off, half-conscious, idle, impassible, imperceptive,
   impercipient, in ignorance of, inanimate, incautious, incognizant,
   inert, insensate, insensible, insensible to, insensitive,
   insentient, late, late lamented, launched into eternity, lifeless,
   martyred, mindless, napping, narcotized, nirvanic, no more,
   nodding, nonconceiving, not with it, numb, numbed, obdurate,
   oblivious, obtuse, off-guard, out, out cold, out of it, passed on,
   passive, pushing up daisies, quiet, released, reposing,
   resting easy, sainted, semiconscious, senseless, sleeping, sleepy,
   slumbering, smitten with death, sound asleep, spaced out, still,
   stillborn, stoned, strung out, taken away, taken off,
   thick-skinned, thick-witted, unalert, unanimated, unaware,
   unaware of, uncautious, unconscious, unconscious of, unfeeling,
   unfelt, unguarded, unhearing, uninsightful, unknowing, unmindful,
   unmindful of, unperceiving, unperceptive, unprehensive, unprepared,
   unready, unrealizing, unseeing, unsuspecting, unvigilant, unwary,
   unwatchful, unwitting, with the Lord, with the saints,
   without life, without vital functions, witless, zonked,
   zonked out