Miss Williams was the Textile Beast. So called because she taught Textiles, and was some sort of beast who hunted anyone who went near her eggs, which she kept in the roof. Eventually it turned out she wore latex feet to cover up her hooves and she could sprout wings if attacked from above. She would lay eggs using a needle-like gland that came out of her anus and she would inject foetusses into eggshells that she made from the bones of those who angered her.
Please note that the Egg Gland came out of her anus.