고 울다

cry at what you watched

The -고 clause is what set the tears off, and here it is usually something watched: 드라마 보고 울었을 때가 있나요? "have you ever cried at a drama?", 김 부장 보고 울었어요? "did Manager Kim make you cry?". 끌어안고 울다 is crying while holding someone. Note the fixed pair 웃지도 못하고 울지도 못하고 — "can neither laugh nor cry" — which is how Koreans say they have no idea how to react.