Now that I've gotten much better at conjugation, I wanted to post a retraction of the 5 sentences I have listed.
As it turns out, the auxiliary verb いる is actually part of the Progressive verb conjugation. This doesn't mean that it is no longer the verb iru. It just means that it is now considered part of the main verb, so it's identity is usually ignored.
A simple way to understand this is to look at the somewhat irregular 五段 verb 有る (ある). It's plain negative form is just the conjugation ない (nai) so it can be written as 無い. That's because, that "nai" is not just conjugation, it is actually the i-adjective 無い (ない). So again, we usually ignore the identity of the i-adjective and just look at it as verb conjugation. This changes, however, when we start stacking conjugation. And that brings us to the 5th example sentence.
The thing that threw me off with 曇らされている is that it's a 五段 verb but the Progressive conjugation was put on like it was an 一段 verb. Turns out, stacked conjugation goes on based on the type of conjugation it's going on, not the verb type. The first conjugation, Passive, goes on like normal: くもらす becomes くもらされる. However, because the Passive conjugation, the auxiliary verb られる, is Ichidan, the next conjugation goes on as if the verb was Ichidan. Adding the Progressive conjugation like so: 曇らされる becomes くもらされている, and there it is.
If you were wondering about stacking on top of ～ない, you would treat the verb as an い-Adjective. That surprised me too.