Can an Arcing Switch Blow a Motor?

I have a little commercial window fan unit that consists of two 120V shaded pole motors hooked up to a metal strip thermostat and a two speed switch.
I ran it yesterday AM, and all was well. When my wife tryed to it on in the afternoon nothing happened.
I checked the cord, switch, put an alligator clip across the thermostat; nothing.
Checked the wiring harness, found nothing obviously wrong, so I removed the fans from the harness, and supplied voltage to each individually (using a handy suicide cord). No spin, both motors are dead. The bearings spin freely, so I haven’t been overloading them.
This leaves me wondering what could cause two motors to burn out simultaneously.
We had lightning, but I’d expect a transient large enough to blow motors would also pop light bulbs, and bother computers. That didn’t happen.
The switch for the unit was pretty cheesy looking, and I suppose that the thermostat contacts might have been arcing. Can this blow out a motor? Is something horribly wrong with the wiring around here, or did I just build up enough karmic debt that highly improbable multiple, simultaneous failures were needed to balance the life force?

IME, an arcing switch generally just blows the switch, but in some cases can take out the motor as well. The electrical storm is also a possibility. Both would have the same failure mode. If the voltage drops, the current will increase. If the current gets too high, the windings “open”. This is a common problem with brown-outs where the voltage drops to a rather low level, but doesn’t go off completely. It can also be the case where there is a relatively high resistance component (like an arc burned contact) causing a significant voltage drop.

To check this, you can check the continuity of the motor windings with an ohm meter. If it reads infinite, there’s your answer.