It would be inconceivable for the woman to lie down while bleeding. The most appropriate thing is to sit down on the toilet and wait.
Lastly, the abortion is characterized by the stimulation of the uterus that, through contractions, induce the expulsion of the intrauterine contents. If you fall asleep, a resting state will take place. This type of state contradicts the stimulation that comes from the abortion, and, as a consequence, the procedure will fail.
Perform your abortion in a good mood, awake and accompanied by a friend. This way, your safety will be assured.