If you say that your arm or leg is asleep, you mean that it is numb, for example because you have been sitting in an awkward position.
(胳膊、腿等) 麻木的
When you fall asleep, you start sleeping.
入睡 • Sam snuggled down in his pillow and fell asleep. 萨姆舒适地枕着枕头睡着了。