Thank you for the response and link. I found Thomas Galloway's explanation and example in that thread extremely helpful.
"I call these guys die pinch creases
They are found on early 20th century rotary press issues. As the envelope blank is fed through the press, there is a line of maximum pressure that is exerted on the die (running from top to bottom). As that line passes over the die, the paper is pushed into the cavity formed by the head, pulling the paper into the center. Then as that line of maximum pressure narrows and moves out the bottom of the embossing die, there is too much paper and it forms a crease."