__work for months ,john had to do whatever___to him

having been out of,表示状态，可以和for months连用,having lost不行 。 was offered 是被动语态。 whatevery引导的宾语从句，要有be.

lost 是瞬间动词，不能和时间段for months 连用，having been out of 是延续动词，可以和时间段for months 连用，
而后面的 whatever 是代替前面的work，john had to do whatever (the work which) was offered to him.offer 用被动。因为工作是被提供给人的。

having been out of,was offered