How an absolute phrase with a passive perfect participle works

I WAS asked this seemingly simple grammar question last week by a member of Jose Carillo’s English Forum who goes by the username Baklis: “While reading your book English Plain and Simple, I came across one of the forms of the absolute phrase—the passive perfect participle. Will you please tell me how it works?”

That question isn’t simple by any measure, though, for the absolute phrase is arguably one of the most knotty and perplexing grammatical forms in English. There’s just no way to explain how it works with the passive perfect participle—itself a tough grammatical nut to crack, so to speak—unless we have a clear idea of how the participle works to begin with.