1 - If something falls apart, it breaks into pieces because it is
old or badly made.
2 - If an organization or system falls apart, it becomes disorganized or unable to
work effectively, or breaks up into its different parts.
3 - If you say that someone is falling apart, you
mean that they are becoming emotionally disturbed and are unable to think calmly or to deal with the difficult or unpleasant situation that they are in.
Ex1: "The
work was
never finished and bit by bit the
building fell apart."
Ex2: "I guess it was like that for you when your company started to fall apart."
Ex3: "I was falling apart. I wasn't getting any sleep."