Armadillos of the genus Tolypeutes, which contains this species and the Brazilian three-banded armadillo, have a carapace with loose bands and unattached edges, and their armour does not clamp down over the hips and shoulders. That slack lets the animal tuck its head and tail into the opening and snap shut into a sphere with no soft tissue exposed. The head shield and tail plate fit the gap like a lid.
Other armadillos are built the opposite way. Their armour is bound closely to the body, and the standard defence is speed and digging: most species will bolt into cover or excavate themselves out of reach rather than curl up. Some can wedge into a burrow so that only armoured surfaces face out, which is a different trick from rolling.
The rolled ball is effective against a predator's jaws, and the species trades away digging ability for it, sheltering in burrows made by other animals. The scale of hunting pressure across the Chaco is poorly quantified, so how much of the species' decline is hunting rather than habitat conversion remains an open question.