Can mean stealing peoples unattended drinks. But it's usually applied to the act of drinking left over drinks in a bar left by other customers in order to get intoxicated on the cheap. Usually done by people who are highly drunk or very poor. Or a mix of any of the above.
Quentin ran out of money, but wasn't quite ready to finish drinking. He mine swept the bar area for dregs until he was sufficiently watered. A group of revellers noticed Quentin mine sweeping and immediately coiled with disgust.