B757-200 Captain reported that a Dangerous Goods agent opened an armed aircraft door to provide the DG envelope. Escape slide fell out of the door but did not deploy. Maintenance was called and door was placed on MEL.

Narrative

Just prior to departure the FO inspected the ADG (Air Driven Generator); handed the agent the signed manifest; waited for the ramp personnel to exit the aircraft then closed and armed L1 and armed R1. He closed and locked the cockpit entry door and returned to his seat. About a minute later we heard what sounded like a short burst of hissing air and out of my side window I observed two ramp agents on the platform of the stairs with the L1 door open. The Dangerous Goods (DG) agent realized she had forgotten to give us the DG envelope and because the inbound envelope was still onboard the FO missed the oversight; so she asked one of the ramp agents to open the door for her. Thankfully no one was hurt; the slide only fell out of the door; it did not deploy; the air we heard was the door assist bottle discharging. I called maintenance. I counseled the ramp agent who opened the door to never ever do that again; if they need to get back onboard they should get our attention through the window or some other way so we can open the door from the inside. The door was subsequently MEL'd and we departed. When we landed in ZZZ; I called the Supervisor as this event hit three different categories in FOM (Any observed hazardous condition; Failure of emergency equipment to operate normally; and; Aircraft entry door slide deployment [unintentional and with or without inflation]). When we arrived in ZZZ1; I reviewed the maintenance history and noticed the following comment from Maintenance Control in the write-up: 'Please inspect slide for any obvious defects that may have caused the prevention of deployment.' It's my understanding the slide should NOT deploy when the door is opened from outside; shouldn't the door be inspected instead for why the slide fell out at all?Cause: Crew not realizing correct Dangerous Goods envelope wasn't onboard. Ramp agent opening door from outside. Slide failing to stay in place when door was opened from outside.Suggestions: Better DG procedures regarding disposing of inbound paperwork. Better training of ramp personnel.