The owners of the other adjacent home have been on an extended vacation (and have left their air conditioning set to 85 Fahrenheit).A few weeks ago, my tenants called me saying that their AC can't maintain setpoint--I assured them that this is normal as both demising walls are currently exposed to elevated temperatures.

@Matt Williams Exposed brick is a hot selling feature right now in older properties...get the fireplace cleaned up, seal it, and showcase it...I'd only consider eliminating it if there is a structural issue......where is your property located?

They have a duty to their shareholders/members to maximize recovery and minimize loss and not exposing the property (REO) to the open market would be negligent in my experience.Maybe you mean working with the owners through their agent or, maybe you mean working with the bank through their agent after the foreclosure.

Given your audience, your role, and your potential liability, I'd do the same in your shoes.But I do so enjoy questioning things, analyzing, looking for flaws, and having my own exposed and corrected. 

Or would they treat it under AZ statute, which would potentially result in ignoring the Series and exposing ALL assets held by the entire Series LLC?

When you start digging out a basement that was never meant to be one, you stand a chance of compromising the integrity of the foundation by exposing or undermining the footers, removing soil that was used for stabilization purposes, etc.

Lots of rot and no soffit at all, which exposed all the ugly nails from the roof.Roof was mostly ok.

For example, if you open a wall / expose and old wiring (specifically Knob and Tube) you must remediate all of it to get any insurance company to give you a policy.

One idea can be worth millions, so get exposed to different investors, books, podcasts, etc. then edit the advice to fit your goals.

Some issues like egress windows or exposed pipes can be fixed and you need quotes for this.