Hello: I really do not think it is a lathe dead center. I worked as both an auto machinist, and job shop machinist in my younger days, and all centers, be they live or dead, were made from tool steel. Now, the other thing that stands out, is no morse taper, to fit a lathe tail stock. If it was a dead center that was chucked up, why this acme thread looking part, and or spring looking piece toward the end? I wish i knew what you have here, but come up empty, especially when you mention the soft material it is made from. Not much help to you, but Good Luck!