After a week of caring for her sick child, she was completely broken down.

broken down 是动词短语 break down 的过去分词形式。break 意思是"打破"，down 表示"向下、降低"，合起来字面意思是"分解、垮掉"。 在句中 broken down 表示"（身体或精神）彻底垮掉、崩溃"的状态，形容极度疲惫和无力支撑的状态。