I bought a trainer at the very cheap end of the spectrum. As we get what we paid for, I opened the box and it came with no skewer...
My bike has skewers with plastic ends (how hard is that plastic is something I don't know), so I'm worried that the trainer can damage my skewers somehow. This answer says it does, but it doesn't explain how (or if I can keep using the bike on the road with the skewer's top damaged). The other answer in the same Q/A says "cosmetic damage".
Here's my skewer:
And this is where it fits in the trainer (if that's relevant):