Start the level from the beginning; the level should start with Tartarus dropping you off on a ledge. An Enforcer gets behind you, but Tartarus drives it away. Continue playing until you get to the point where you drop down a piston tube and see no enemies, but evidence of a conflict. This area has multiple crates of weapons and bodies lying about. If you walk to the ledge facing out of the stage and look down, you should see a Phantom floating there, several levels below your current location.
Drop down the piston in the center of the room; as you fall, make sure you stay in the center of the tube. When you approach the end of the fall, there will be a bar going across the exit. Land on that bar and nothing can kill you -- not even the three waves of Flood Infection Forms that come out of the tube after you.
The glitch is probably the result of a safeguard that Bungie may have added. Such a safeguard would prevent players from dying from fall damage by making them invulnerable until they reached the bottom of the shaft. If this is the case, then the trick is more of an exploit than a glitch.