This large, white creature appears to be quite threatening, but, like many of the larger characters in Yume Nikki, it does not interact much or pose any threat to Madotsuki.
It has a large, amorphous body with four indeterminate limbs, a large eye and an appendage that appears to be a large, quivering jaw or mandible that makes a constant rattling sound.
The Thing with the Quivering Jaw does not move (besides its quivering jaw) or interact with Madotsuki. The jaw can be stilled using the stoplight effect. Like many non-NPC characters, it cannot be killed or interacted with the knife, and is not drawn by the Cat effect.
The Thing with the Quivering Jaw is quite an imposing character that many players find frightening or unappealing. Its deformed body structure with the sharp teeth make for a sudden fright when the player enters the room. Its lack of movement also puts players on edge, as it seems to be about to attack.
The door to the room is part of a large mutilated head consistent with many parts of the white desert that have body parts emerging from the floor. In this room however, the sprite creates a slightly different image that looks as if it may be part of a person that was killed and being eaten by The Thing, but was interrupted when Madotsuki appeared from the remains of the body. The head also resembles that of the Buddha.
It may have a connection with Monoko, since they both are in the White Desert and have multiple deformed arms (including the arm in the head, with the noticeable vein).