首先要纠正你的不规范的说法：这里,而且在英语语言中都不存在什么“非谓语从句”,只存在“非谓语动词或短语”.
就你这句而言,应当这么说：
(Having been) Being exposed to unlight for a long time was...
因为 exposed 是 adj.不可以直接做主语,因为做主语的必须是“名词、代词或相当于名词或代词的词、短语或从句”.
因此必须将 exposed 转化成可以做主语的动名词：Being exposed to...was...
因为 Being.本身是可以表示“持续或延续的状态”的动词,可以和一段时间 for a long time 搭配,所以不用表示持续状态的 Having been.也可以,而且更加简练.
通常,to have (been) done,也 不定式的过去式,即相当于说“...did/ had done sth",表示一个比句子动词 “更早的”过去动作,如：
He is said to have studied in the US five years ago.
= It is said that he studied .
He was said to have studied in the US five years before.
= It was said that he had studied...five years before.
这里不需要也不能用什么 To have been being exposed to.