The crew holds the righting line in their back or "aft" hand, as it is solidily attached at the stern of boat. When you suddenly slow down, this will give the crew something to keep them from falling forward. A stiff back leg will keep them from falling backwards during sudden acceleration, a much less common occurance.
My son/crew ended up in front of the crossbar when I stuffed the leeward bow upwind last Saturday
, he thinks his "cat like" (pun intended) reflexes are quick enough to prevent this and besides "the A-fleet crews don't use it". Your crew definitely wants to keep the righting line in hand, there's no chance of grabbing it on the way.