Ok, You are correct in that I did not consider the possibility of an embedded \r.
"Unless you are using binmode, you will never see a <CR>". should be:
"Unless you are using binmode, you will never see a <CR> as part of the line ending".

Your code shows this: "x\ry\r\n" becomes ""x\ry\n". The <CR> associated with the line ending is taken out. This is not a global deletion of just any <CR>. It is a modification of the line ending sequence, just as I said albeit not as perfectly qualified as it could have been.

From reading further info from the OP, it appears that this some kind of strange cygwin issue. I used to have, but no longer have a cygwin installation. cygwin is a weird neither beast nor fowl thing. Once I found out that I couldn't really run SW that used Unix specific features, I got rid of that thing in preference to simply using windows ports of some of the Unix command line utilities.

PS: I did not know if $/ could be set to "\r\n" or not and I said so. I did not give either a "yes" or a "no" answer. You show that it can indeed be set to that. Great to hear that additional info!