Quote Originally Posted by scotcher
Literally:

To become untied, unfastened, loose etc.

The rope came undone = the rope became untied
Her shirt came undone = the buttons holding her shirt became unfastened.


Figuratively:

To fail, to be brought to destruction or ruin.

All his plans came undone. = all his plans failed.
Emotionally- to become extremely sad to the point of despair
As in "When he left her, she became undone and took her own life."