What does “butjapda” mean in a Korean breakup?

붙잡다 is 붙다 (“to stick”) plus 잡다 (“to grab”), so its base sense is holding something so it can’t get away. Point it at a person who is leaving you and it becomes the verb for begging them not to go: 헤어지자는 사람을 붙잡다, “to hold on to someone who wants to break up.” No single English verb carries that whole scene.

In the clip a woman describes the three years after a long relationship ended: 계속 막 붙잡거든 내가 — “I just kept holding on.” The literal senses stay useful too: 팔을 붙잡다 (grab someone’s arm), 택시를 붙잡다 (flag down a taxi). The passive 붙잡히다 is what happens when the police catch you.