In the case of the Caracalla I posted, its the one I spoke about in another thread that I purchased as a whole coin, but it arrived in the pieces you see in the image. So, in this case, the postman did it!
They can be. Some the metal has become brittle over the millennia's, while some are not packaged well enough for shipment. I've even read here on CT where someone has dropped a coin (on carpet I might mention) and the coin broke. In these cases I assume there was a crack running through the flan.
I chose a couple of broken Roman and Greek coins. They represent Constantius II and Berenike II. They don't look really ugly at all to me !
There are many collecting themes. This is just one of them. I like things out of the ordinary. Yes, common enough, but rarer than intact coins. Some are broken in modern times due to handling, excavation, etc. but many are broken in ancient times to make small change when low denomination coins were not available. I just got this Nero sestertius in today's mail: