A lot of good guesses and ideas. I would say the idea that taking a part of the statue might be a hint or close to what the truth actually is.

Maybe its as simple as breaking off a piece and carrying it with you.

Though it could be multiple things, like disabling the trap at the entrance, the statue piece, killing all or none of the monsters, finding the hidden mcguffin in the dungeon and a hidden exit. Could be even all the dungeons follow this pattern.

Though if killing "all" the monsters makes it impossible to continue, I'd assume it has an auto respawn system somehow. magic, a wizard did it, possibly with severl monsters to repopulate the place. eew.