I've encountered skunks in the wilderness a couple times. They stop, I stop. Their tails go up as if to say "is this going to be a thing?" and I back slowly away. Their tails go back down and we go about our business. Skunks are effectively immune to wise predators. Most dogs get sprayed once. Golden retrievers often get sprayed over and over. I lived next door to a 90lb doberman cross that got sprayed once, ate the skunk, developed a taste and spent the rest of its life seeking out skunks. That dog was evil.
I was sprayed one night while walking down an unlit trail. Only saw him momentarily just as he sprayed. I do not generally mind the smell of skunk but it was so ridiculously strong it made me nauseous. I had someone retrieve several gallons of tomato juice to soak in and I slept on the porch but still reeked for 2 days. My clothes fluttered in the wind for a month but did not recover so I threw them out along with my wallet. Good times.
When I release squirrels and woodchucks, they bolt once they can squeeze out. The skunk took his time. He eventually sauntered out, paused, then started looking about as he slowly meandered away. I would imagine their chill nature is part of their defense. Predators likely have an instinctive wariness of things that look like prey but don't act like prey. That might partially explain this bear sleeping thing: It makes me wonder if there's ever been a study regarding bear/cougar attacks on humans, and the clothes the people were wearing. You might look like nervous prey in natural colors/camouflage, whereas an 80's neon jacket might make you look like an enormous noxious caterpillar.