Without any more information, we’re only guessing. The good and the bad cases could have come from two different rifles, for all we know.
Short headspace would leave the head of the cartridge hanging out of the chamber, unsupported, causing it to bulge, at worst to rupture, and at best leaving what looks like a belt or rim. With excessive headspace, the cartridge would be seated deeper in the chamber.
If the chamber was cut for a rimmed cartridge of nearly the same length as the .30 Carbine, a Carbine cartridge would seat and fire and the head expands to form a rim.
I’m like you. I don’t see how a Carbine could fire a cartridge that’s not fully seated unless the firing pin was broken and frozen in place. The carbine design simply does not allow the firing pin to go forward until the bolt turns and locks in place.
Interesting cases, either way. It never ceases to amaze me what you can find at a public rifle range. I’m a very conservative shooter and when anything unusual happens, I will stop immediately. Others will shoot several more times just to see if it keeps happening.