I have never had this happen before. A new 30-06 Seating Die, first use, cleaned with alcohol, closed the ram with the case on the bullet, and at withdrawal of the ram, expecting a seated bullet on the case, the bullet stuck in the Seating Die and only the case withdrew!
I took the Seating Die apart, screwed the seating stem upside down in the die body, held it in place for the shot through the center hole of the ram, and took the picture.
I used the Hot Glue technique to make the die "fit" the bullet and that worked perfectly.