I have a $1 bill series 2001 with what appears to be a piece of the bill underneath of it from the sheet. Or it could be from an uncut sheet and someone just didn't cut it all the way. The bottom margin isn't a straight cut either. Here's a pic...
Typically, one can tell if a bill came from an uncut sheet by the high serial numbers. When a cutting error for lack of a better term arises, the first place to look to see if it is a "man-made" error or one made intentionally is the serial number. Post the serial number and we can likely be of more help.