This error is in the same family as die crack.
The broken die is distinct, because it occurs only on the rim and may contaminate the field. However, to be called a Cuds, it needs to start from the rim.
When part of the die on top is completely broken, it will probably fall fairly quickly, either by gravity or the comings and goings of the press, from top to bottom.
If it's a part of the die at the bottom, it can remain in place longer. In addition, there is the collar that surrounds and may play a wall to hold the broken part. This will produce on the coin a growth or swelling. Also, there will be no design on this part of the coin.
This error can be called Major Cud break or die or DEB or Die edge break.
Picture: Ken Potter