Be ill,she went home.和Having finished their work ,they had a rest
问题描述：
Be ill,she went home.和Having finished their work ,they had a rest
答
Be ill = She was ill.
Having finished their work 做完成分词引入的状语,表示该行为在主语行为之前完成.
可以看做为：Since they had finished their work,they had a rest