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 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 . Oh yeah, 30-06, RCBS die, Midway 150 grain FMJ bullets.