Picture a ball of string being unraveled by a cat. Figuratively speaking, people become unraveled too. Often it's when their integrity gets questioned in some manner and they lie, and then tell another lie to protect the first lie, and so on. And these lies wrap themselves together into a ball around the liar; tighter and tighter. If someone was to pull one of the loose threads, it would grow longer and longer. A string of deceit, unraveling the very person themselves. Becoming unraveled.

It usually refers to anything that is "falling apart" and the expression comes from knitting, when the "stitches" are coming undone and the garment is turning back into yarn.