I owned up to a collective offense a few times when I didn’t need to, just to get the slipper (which left a nice warm glow) but I never did so if there was a risk it would be the cane instead!
I remember at one of my schools one boy who was regularly caned by the head teacher, and he didn’t seem too upset about it. I’ve long wondered if there was some kind of sadomasochistic bond between them.