Constrictors kill by wrapping their bodies around a victim, not by grabbing the head.
Then again, many snakes do eat carrion as well.
Some constrictors will swallow their live prey head first. I saw a film on Youtube a month ago of a King snake (a constrictor) killing and eating a rattlesnake. The King snake entered the rattlesnakes den and swallowed the rattlesnake head first without first constricting (killing) the rattler.