Digital electronic equipment in computer systems all have a definite "on" state. Even if there is no mechanical moving parts in the machine, digital circuits still have various states. Every action performed by these digital circuits are essentially a transition from one state to one or more other states. If there is no power going to these circuits, they are off, which means essentially (to use an analogy) trying to get the computer to talk to it and get a response would be like trying to have a conversation with a dead corpse.
When a computer turns on, all digital circuits go through an initial state. It's typically called "reset", where all the random electronic charges in the materials are cleared out and the circuit enters a stable initial state, ready to perform its function when state changes are triggered via its input(s). This would be analogous to a HDD spinning up. It's changing from its resting state to a state of readiness.
So, yes, they have a definitive on/off state. They have to, since it's not just the storage medium but all the supporting electronics that allow us to read and write to them.
Update for the OP update
Yes, it likely uses less power when off. The thing is that it does not have to power a motor like a HDD does. A HDD will spin down when idle to conserve power (if you set it to). The only reason to keep it spinning is so that you don't have to wait for it to spin up before you can read data, which can take a second or two. But with a SSD, there aren't any concerns with things like that. It will consume power so that it may accept read and write requests, but it likely won't be consuming as much power as when it's processing read and write requests, simply because it is using less circuitry, and therefore, using less electricity. It will not be using any electricity when turned off, because (like all the other components in your computer), the motherboard would have told your power supply to cut off electrical current to the device. When turned off, unless you have a very old computer, the only electronic device in your machine to receive power will be the motherboard, and only just enough to monitor the power button. The power output to the drive will be outputting very little, if any, electrical current, in this state, though.
My guess is it broke a data connection from the usb to the internal board.
It shouldn't cause any damage to your laptop, unless it were to have shorted out something electrical that would cause a surge to go back through usb into your laptop. My guess is this didn't happen, I would expect a surge would cause the motherboard to immediately shut your laptop down.
You might try opening the thumb drive plastic shield and inspect for broken solder points. It wouldn't be that difficult to attempt to resolder the point if there were one broken, likely just have to melt the solder enough to "jump" it back over.
Best Answer
Here is a paper about errors caused by power failure on flash memory: http://cseweb.ucsd.edu/users/swanson/papers/DAC2011PowerCut.pdf
I cite the last sentence of the abstract:
and the conclusion of the paper:
My personal conclusion is
Power loss in general can render flash memory in an unreliable state. However, once you hard erase, the memory works as good as before.
Carefully written firmware can fully prevent errors on power loss but at a performance and lifetime cost of the flash memory as writes have to be protected by extra writes.
Many vendors offer hard erase utilities for download. But I think there are flash memory devices that do not allow you to do a hard erase and also will not perform a hard erase themselves and also do not employ a perfectly safe write protocol. It follows that these can be rendered effectively unreliable or unusable by power loss during a write even if they are not damaged physically.
If you really want, you can take an "effectively unreliable or unusable" USB memory and move (i.e. desolder and reconnect) its flash ICs to an environment that allows hard erasure. The flash ICs should be useable again now.