Probably a fixture for repeat work? If it's welded and doesn't unscrew out of the collet, then it was a setup-once-and-useforever sorta thing. Do the metal bars either side of the round hole move? that would make it a clamp.
Can't adjust anything, diameter is .375, flats are .312 , the set screw in back serves no purpose? It is welded in near the rear threads. Could it be something a gunsmith coud use? Cleaning out and don't want to throw something out that someone can use.
Set screw is probably an artifact of whatever arbor was shoved into that 5C collet. Perhaps it used to be an end-mill holder or was an arbor extension or something.
So, the opening does not adjust, meaning it is for a specific size and shape part (or tooling). Is the hole a through-hole? or is there effectively a depth-stop?