Spinning lug nut.....how can this be possible?

My old Dodge pickup has stainless covers over the nuts. Over time the steel nuts rust to the point the cover expands so the right size socket will not fit. When you go to larger size, the socket will spin without turning the nut. In with my tire changing tools I carry a tool designed to remove rounded nuts, and enough nuts for one wheel. I tried like bell to find solid nuts, but could not match the wheel end....