We investigate reversible inverse magnetostriction in order to study scaling properties of magnetic hysteresis in the helical antiferromagnetic phase of polycrystalline Dy. We argue that the experimental method used is more sensitive than studies of conventional magnetic hysteresis. This advantage allows us to study hysteretic properties of antiferromagnetic Dy over the temperature ranges, not accessible previously. We introduce generalized coercivity of magnetoelastic hysteresis and show that it demonstrates, under different experimental protocols, the same exponents of scaling power laws in the ferro- and antiferromagnetic phases. The similarity of hindering mechanisms impeding the mobility of domain walls in antiferromagnetic and ferromagnetic phases is suggested as the reason of the observed universality of hysteresis scaling.