Almost from the very first Systema session you take part in, the importance of being comfortable on the floor is made clear. Being comfortable on the floor of course means being able to work on the floor in a ground fighting (or you may call it wrestling) situation. However, the point that is made to the new student is that one should also be comfortable going from standing up to the floor and back again in a smooth way with as little chance of injury as possible.
It is quite commonly known that fights can be over very quickly and it is also quite possible that the fight can go to the ground either because one is pushed there, or the people involved fall together or the environment e.g. chairs and tables conspires to push you to the floor.
However it may happen, one needs to develop the awareness to hit the floor as softly and in a controlled fashion as possible but at the same time initiating a sequence of motion that will bring you back to your feet as quickly as possible.
We always teach students to put their hand behind their head if going backwards onto the floor to protect the head from the impact. We also teach how to roll onto the floor using soft movement and breathing. If you visit a Systema club you will very likely see a set of mats out as with any other martial art that works on the ground, but you will very likely see some students happily rolling, dive rolling and transitioning back up to their feet on the hard uncovered floor. That skill in many cases can be displayed on hard surfaces outside such as concrete and tarmac.
It can take a while to develop these skills, however it is a crucial part of the physical and psychological make up to survive in a violent confrontation on the street.