I can't even imagine how that could possibly happen...
I do not suggest that athletes can do this, 'omnidirectional stability'.
Ok, I think I'm done then.
I will leave you these diagrams as food for thought, each picture represents a different person (of hypothetical origin, not referring to any specific person) with a different degree of ability (displayed in ascending order) at receiving incoming force from any angle standing in a posture to receive the incoming push; a brief description of their level is below each picture.
Since the force vector is unknown I've left the arrows off the pictures (I'm also no artist!)
I don't feel qualified to discuss the inner workings via an online medium so I'm going to resign from the discussion at this point; best of luck in your training.