I do not find many hi denomination error or keeper notes, but here is one I found which surprised me...
Here is one which I am unsure that the overprint is not from outside the BEP. However, BEP Cloth Batting has sometime looked like this...
Your paper fold was during the first print and then unfolded for the second and refolded for the third printing as detected by the separation in the "0" and not the back. Interesting. I will have to look at mine and get back to you.
My gutterfold is a 2009 $1 FW and I cannot determine if it did the same as yours, but the back is intact.