En-caul birth occurs when the baby is born inside the entire amniotic sac. The sac balloons out at birth, with the amniotic fluid and child remaining inside the unbroken or partially broken membrane. While the appearance of an en-caul baby might look worrying, the caul is completely harmless and won’t suffocate the infant. The baby breathes through its placenta, which is still attached to its mother. In this case the baby is being born via cesarean section. The thin but durable membrane filled with fluid is what helps keep the baby warm and safe from bumps during the entire pregnancy. It can be easily removed by the attending physician or midwife. Being born ‘en-caul’ is extraordinarily rare, occurring in fewer than 1 out of 80,000 births and mostly happens in premature babies.
I've seen one that gave birth naturally but the baby was in the amniotic sac...