The Fire-Mouthed Woman is a Novelization-exclusive monster, that is just what the name implies. She most certainly was released during The Purge.
Physical Description and Attributes
The Fire-Mouthed Woman is a monster in the Facility's possession, which is literally a woman with fire dripping from her mouth and nose. She is one of the 'Unblooded' Monsters. She only appears in the 'System Purge' chunk of the book where she is mentioned as one of the 'Unblooded' monsters exiting the elevators during the Purge.
References
This Monster may be a reference to many monsters' 'Breath Weapons', like the common fire, thermonuclear breath, etc.