It took some persuasion, but she eventually came round and agreed to the proposal.

came 是动词 come 的过去式，come 的基本意思是"来"。 round 在这里是副词，表示"转变方向"或"改变立场"。 came round 是一个短语动词，意思是"改变主意"或"回心转意"，指从反对或不情愿的状态转变为接受或同意的状态。