1
general::
Phrase(s): fall asleep
Fig. to go to sleep. • I fell asleep while reading the very dull book. • I got in bed and fell asleep at once.
McGrawhill's American Idioms And Phrasal Verbs
2
general::
Go to sleep; also, cease paying attention. For example, As soon as the lights were dimmed he fell asleep, or His lectures are so dull that I fall asleep. The literal usage, which uses the verb fall in the sense of "succumb," dates from about 1300; the figurative is several centuries newer. Also see ASLEEP AT THE SWITCH.
American Heritage Idioms