Emotional distress. Breakdown. If in our normal nature we are ‘whole’ than to fall to pieces means we are broken. Imagine a jigsaw puzzle tossed on the ground and falls to many pieces, so this phrase implies that someone’s anger or grief has torn them apart emotionally or physically. (Compare  to Break down, Off the deep end, Snap or Shock to the system.)

“Ever since he wife died, he has lived poorly and frankly, he’s gone to pieces.”