Here in Western Illinois I have no hard numbers but I’d say less than 10% of the hay is stored inside. It’s almost all large rounds and some do wrap them in white plastic but most don’t. I’m surprised when large rounds are broke open that look old the inside will look good.
No for sure there is probably 6” of rot which is honestly a good bit of hay. But that’s about it, no bales below it. The shape does repel. Big ole flat bale would soak up I would think, then migrate in wards.
Much of it will depend upon your weather conditions and soil types.
I have been around a lot of Western irrigated hay that is stored outdoors, years ago that would have been small squares now it's large squares. In those arid climates the hay will stay quite good. If stacked on bare ground the bottom tier will be moldy and bad at least halfway up, the top tier will have bad hay for 6"s or so.
However in the NorthEast with it's much wetter and higher humidity numbers year round the amount of loss will be much higher.
Poor quality hay ground or chopped up and mixed with good feed will allow cows to sustain and stay somewhat healthy.
Older brood cows can survive on poor quality hay, if they are still nursing a calve that calve will not do as good as a cow getting higher quality feed. Older brood cows can actually be over fed on high quality hay with good digestibility and high protein (early cut prior to maturity), and get to fat and have troubles calving.
Dairy animals especially producing milk cows will do quite poorly on low quality feed and it can actually taint the taste of the milk, as it can effect the flavor of beef animals.
I calculated the rough amount of feed lose on a round bale previously but here we go again just for sh*ts and grins.
Start out with a big round bale 5' x 5' which would be approximately 98.17 cu. ft..
Reduce the size by 6" all around including the ends so now we are down to a 4 x 4 bale which is about 50.27 cubic feet,
dang almost a 50% loss of feed or twice as much money for the same amount of quality feed.
Many people will say that the waste is much less, OK.
Start out with that same 5x5 round bale, lets only have 2" of waste on the ends and lets say the bottom has 4" of bad feed the top and sides only 3" so lets use 3.25" for average loose.
54" x 53.5" which ends up with 70.25 cu. ft. of good feed or about 3/4's of what we started with.
Just my feelings and opinion from handling a lot bales both small square (mostly 2 twine bales but some 2 and 3 wire bales) and round, and feeding animals for several decades.