Well, some of the mystery is solved! The white parts started drying, becoming thinner, turning dark and then fell off. They are seeds!
I still think I must have cut the pod so the seed production was exposed. I will plant them just for fun but know that I won't get flowers for years! The last two flowers on the plant also had pods and I am in the process of watching them dry, with the dead flower still attached.
I t's like a little science project!