To me a "complete break" means rim to rim. A die that has broken rim-to-rim but stikes a coin with the broken piece retained in place so that the broken piece of the die strikes up the design on the coin (maybe weakly, maybe fairly strongly) produces a retained cud (that includes the rim). A die that has broken rim-to-rim and the broken piece has fallen away (or otherwise is incapable of striking up a coin) produces a cud (that includes the rim).