Ok, point one, coming round from anesthetics can cause any number of issues with the wig, but I think a strong bond will negate most of these. I've seen plenty of patients restlessly trying to climb out or their hospital bed, or attempting to climb over the cot sides. Remember, coming round is the weird part as it’s not like waking up from sleep, it’s like when you are so tired you can’t keep your eyes open, bobbing your head etc, & many patients even struggle & thrash in the bed. Also you may be a patient who needs intubation before, during, or after the op, so the tube (or indeed an oxygen mask) may be held in place using elastic cords that go round your head.
Point two, I personally would always tell my anesthetist because the operating room is a totally sterile environment. If a hairpiece came loose and swung down touching the instruments, the whole set would be contaminated and the operation would be compromised leading to a longer than expected procedure due to opening a new set & staff re sterilizing themselves. Both worst case scenarios for sure, but these are my observations and experiences.
Regards