The vinyl on old cars was thick stuff but it still cracked and split. Two things would happen, the vinyl would stick up and cause a sharp edge that would get you. We used scissors to cut the offending edge off. The other was that the crack would pinch your legs. Especially painful when wearing shorts. We used nylon tape for that. This was before duct tape.
On really old cars with coil springs the spring tip would come through and puncture the vinyl. This required wire cutter dikes to cut the offending spring back.
Same thing happened with furniture as well. The old Naugahyde never held up well.
