back in the 50's in some parts of the country it was standard practice to install cardboard. I'm guessing it was an attempt at air sealing and to help hold the insulation in place, especially blown in cellulose. polyethylene sheeting was not common, nor were all of our more modern materials.
I actually have it in my home in the attic that separates dormer walls from the unconditioned attic space. the cardboard is lapped and secured on all four sides to the wall framing.
"You get what you pay for, and sometimes free costs more!"