You’ll know if you’re about to enter the Looping Hallway when you see a stack of desks almost blocking a door.
Upon entering, you won’t see the wire anymore. Instead, follow the hallway to find a billow of white smoke. Approach it but don’t go through it.
Turn around and you should see the breaker that’s previously not there. Interact with it to remove the smoke.
Go past where the smoke was earlier to find the red wire on the floor again. It will lead you to another breaker that’s connected to the exit gate. Activate it to leave the hallway.