If I'm not mistaken, everyone from the known monsters (from the ones that we can choose from, Sandy, etc.) knows that the gym teacher is a werewolf. However, Sandy does say that there is another monster in the school if you play as a demon. Although I don't remember if it was stated to be a teacher tho, I do however suspect that it's a new monster in the town and they will be connected to the disappeared student in a way.
A bit off-topic. I'm not an OverWatch player but the second I saw the name "Genji" in the name choices for the Demon path, that immediately remined me of Genji Shimada from OverWatch. Let's just say that I recreated Demon!Genji with red hair for laughs and giggles. Geez, this sounds like a bad fanfic now that I think about it. Good job regardless, Creator.
Anyway, I remember hearing about a current monster that kidnaps children/people at night. Was it the trolls? I don't remember the name but I remember that the parents used to scare the children by using that particular monster.