Witch
Witches are one of the monsters seen listed on the whiteboard. Operations bets on them.
Physical Description & Attributes
They are depicted as powerful women, having snow white hair and pale skin with the abilities of flight and levitation.
A witch can be seen in the first wave of the Purge snatching the soul of a security guard before flying off. It looks like a bolt of light neon blue rays running through the victims bodies. The same witch is seen later on one of the monitors in the Control Room, casting a sort of binding spell on a woman attempting to run from her.
It is possible that a broomstick summons them.
It's also possible that they are bullet proof but very vulnerable to fire and explosives.
Inspiration
Witches have been a staple character in horror stories and Halloween folklore for several years with the main iconic image going back as far as the Grimm's Fairy Tales of the 1800s, such as "Hansel and Gretel," a fairy tale loosely based on the Slavic tale of Baba Yaga. The origins of witches actually date back to pagan folk magic of from Ancient Europe, later distorted and corrupted by the later Christian Church erroneously distorting it into a form of devil worship. Witchcraft is still an active religion today under the New Age movement.
A witch stealing the soul of a security guard.
The stereotypical witch of legend is generally depicted as an ugly old woman having long white, green or blue hair and wearing long black dresses or cloaks and a conical hat with a brim, a holdover from the witch persecution of the Middle Ages. Among their powers, witches were believed to cast spells and curses, turn themselves and others into animals and to fly on a long stick, usually depicted as a broom. They were usually represented by a cat, which was considered sacred.
A witch in her cube during an early version of the elevator scene.
The witch seen on the movie was very likely based on Haggis, from Pumpkinhead or the Evil Queen from the Disney animated movie Snow-White and the Seven Dwarves.