Sorry - memory skipped the round versions.

There was an "Econ" fodder roller, which did not use any tie string or net, only about 3ft round and maybe 4 wide. Just relied on the length of the hay to give a 'wrap' that was reasonably waterproof.

Then various large round balers -  many still used these days.  Some round bales are silage, rolled at high moisture content, and air tight wrapped in plastic.  Sort of shrink wrap ??