Note that falling safely when expecting to be thrown is not the same as landing safely when falling unexpectedly. The latter is probably a special skill, not specifically trained for in martial arts. Here is some discussion:
Breakfalling may even help you get through a training session where you get tossed around a 100 times or more. But, when you slip and fall off the mat your training will most likely not kick in and save you.
Note that falling safely when expecting to be thrown is not the same as landing safely when falling unexpectedly. The latter is probably a special skill, not specifically trained for in martial arts. Here is some discussion: