It’s probably nothing dramatic, but that was always drilled into my head as a possibility, and I still check my shoes before getting on.
It would snap off. Whether it injures your foot is going to be a function of how strong the lace is and how your shoes are laced up and the pressure it would put on your foot as it got wound into the mechanism. Short of a big nylon boot lace I don’t see any regular shoe lace as being capable of injury in that mode.
This happened to me so recently this topic title spooked me. I was wearing ordinary trainers at the time and it was one of those ramp escalators you can use trolleys on; my shoelace got pulled very tight and was well and truly stuck in between some of the teeth at the base of the escalator, and a couple of strangers had to help me out (I had images of having my leg ripped off floating around my head). The shoelace didn’t break, and I suspected it would have broken long before I was injured.
Even if the laces are made of really strong cord, I expect they would still probably part where it’s caught on or against some metal parts.
If you notice the lace is caught, you can always just jerk your foot upward as hard as possible to reduce the “boa constrictor” effect of the lace tightening up your whole shoe. Just snap that bitch like a Slim Jim. 
Crocs and open-toed shoes appear to be much more dangerous but it’s not uncommon to read reports of lost toes or sprained ankles resulting from loose laces on escalators. The Snopes entry is mainly on Crocs but touches on shoelaces as well.
If anyone needs to know how sick the universe can be, I once witnessed a the seeing-eye dog of a blind person get its paw caught in an escalator.
Damn, now that is messed up.
Fortunately somebody was able to hit the emergency stop pretty quick. The dog was shrieking like a banshee. Its paw was badly pinched but they were able to extract it after maybe 30 minutes. I’m sure it hurt like the devil but I think it was probably able to recover without any serious permanent damage.
But come on, universe, that’s just being mean.
Shoe laces are strong enough that you could be injured. People do successfully hang themselves with them.
They seldom break where they are caught. If your shoe lace gets caught in an escalator snap your foot and try to break the lace. If it does not break get your foot out of your shoe before it gets pulled into the skirt or under the tread plates. It is ugly when a shoe gets caught in an escalator skirt and it does not have skirt safties or they do not work.
The older ones are direct drive with 5 to 15 hp motors. Your body parts will not stop them.
I am always have a hard time believing how stupid people can be around esclators. It is like there is a bucket at the top and bottom to deposit your brain before getting on.
When I was young I carelessly caught the skin between the thumb and index finger caught in a grocery store conveyor belt. I wouldn’t care to repeat that experience.
What would happen if my shoelace got caught in an escalator?
There’s a big bucket underneath the escalator to reception the sausages.
Apparently there’s a brain bucket as well.
Great, now I have something new to worry about!..TRM (suddenly remembering a brief passage from “World According to Garp”)
My daughter was wearing Converse All-Stars on an escalator in Chicago, and somehow, the rubber part over the toe got caught in the teeth at the top. It ripped the shoe apart, and to this day, we have no idea how it happened or how she escaped without injury.
Miss alignment of the of the upper landing. Depending on the brand, upper carrage bearings in bad shape, step chain worn badly. Broken comb plates.
Never let your feet be pushed accross the landing, always step off.
Huh, I had no idea this could actually happen. Guess I’ll be taking the stairs from now on.
I don’t really understand what the shoelace gets caught on, though? What is visible of the escalator “stairs” seem to be smooth with some ridges, nothing that would hold a shoelace.
If the shoe lace slips between the steps it can get caught in the moving step chain. At a landing it can get caught between the landing and a step. It will not always happen but it can.
I always love people who will not get on a elevator (a cable elevator is one of the safeest things around), but will head straight for an escalator. Next time you ride an escalator notice how many moving and stationary places are exposed to the public.
We can send a man to the moon (multiple times) with no casualties but we can’t invent an escalator that won’t turn body parts into Spam!?! WTF!?!
It’s because we’re an organism that forgets how to walk when we’re on said escalator, and forget how to get out of the way of those who haven’t forgotten how to walk to boot.
I’ll let pass not walking on a step type escalator, but everything else gets a frowny face.
As long as there are moving parts next to stationary parts exposed to body parts then there is a danger.
As far as the “send men to the moon”. On ecsalator costs $1,000,000,000. Wrong comparison.