(1)doing 为动名词主动形式

(2)being done为动名词被动形式

备注：动名词属于非谓语动词可以作句子：主语，宾语，表语，同位语，定语，补语

He is left alone at home 

解析：is left为谓语动词，只能作句子谓语成分

He doesn't like being left alone at home

解析：being left alone at home为非谓语动词（动名词短语）作句子宾语成分

Being left alone at home made the boy annoyed

解析：being left alone at home为非谓语动词（动名词短语）作句子主语成分

备注：

(1)being left alone at home为动名词短语，可以作句子主语，宾语，表语等成分

(2)left alone at home为过去分词短语，只能作句子状语，定语等成分，不能作句子主语成分，所以不能去掉“being”