Work softening, is the correct term. Some metals work harden,and if they do, it happens instantly upon deforming the metal. Brass work hardens to a much higher hardness than mild steel, so hard in fact that it will even damage a ball or roller bearing race. Yet ignorant people purchase brass hammers to beat on their steel guns and other precision things they don't want to damage, when the soft hammer should be lead alloy, copper, pure aluminum, or mild steel, in that order, with last hardest. -- I just threw that at you out of my basket of machine shop tricks, as I think we all should get all the knowledge we can. Especailly this tidbit being so important to gun owners who work on their own guns.
SOFT lead work hardens instantly when worked, by crushing with hammer blow or whatever. When hardened lead alloy is worked, as in sizing, I don't know if there is an instant work hardening, but I do know that the deformed metal softens AFTER being worked, and softens quite rapidly, like a day or three. In other words it will be soft before most people will shoot them. But only the tiny layer which is actually deformed is work softened, a few thousandths deep. The rest of the bullet retains full hardness, which prevents bullet obturation and deformation under the pressure of shooting, relitive to the bullets hardness.
The work softened skin has no effect whatsoever on the velocity one can obtain before leading begins, nor on accuracy at those high end velocities. (Or slow speeds.) So, for the bullet caster knowing that your hard bullets are work softened by sizing is information we would be as well of not knowing. --- Better to know which metal to use to make a soft hammer!