Not born without amniotic sac, but rather born with the amniotic sac intact.

This is called an en-caul birth and there is a lot of very old superstitions about people born en-caul, mostly that it was good luck.

Ah, yes, I read 'sans' rather than 'dans'. Thanks!

A baby "born under a caul". A rare occurrence, it was taken as a sign of extremely good luck in many cultures a long time ago.