Probably vinyl wallpaper.
That puts the moisture barrier at the inside surface of the wall. All moisture being driven into the wall by wind, weather, air pressure differences, etc., ends up "in the wall"m which is also most likely filled with batt insulation.
I'm going to guess that the batt insulation is saturated with water. (I've seen it.) Do you have a hygrometer (
Thermo Hygrometers ) to read humidity with?
If so, make a small hole in the wall and insert the end or your hygrometer into the wall cavity. I've found as much as 99.9% RH (the maximum the meter can read).
The problem likely comes down to building science and dew point in the wall.
The outside is warm, the inside is cold, somewhere between there is where the dew point will be. If the dew point is at the outside of the wall, the condensation will drain down the outside of the wall and not be a problem. If the dew point were on the interior surface of the wall, the condensation would be collecting on the interior surface of the wall and would drain down the face of the wallpaper.
However, the dew point is likely "within" the wall, and is likely near the back of the gypsum board behind the wallpaper. That means all the condensation is collecting in the insulation, which becomes saturated, gets the gypsum board wet, and gets the paper facing on the gypsum board wet (both sides of the gypsum board).
In all likelihood you will find that moisture is penetrating through the wall more than it is intended to. If it is a metal or wood stud wall, with DensGlass Gold sheathing, covered with stucco, it is quite possible that the systems were not installed properly, possibly even that the wrong lath was used. Possibly used standard paper-backed metal lath when they should have used either furring strips or self-furring paper backed metal lath.
Also likely that the DensGlass Gold is not installed and sealed up properly. When done properly, it does not (per the manufacturer) require a building wrap. Being as no one ever 'does it properly' a building wrap is really needed over the DensGlass Gold before the paper-backed metal lath, self-furring type, is installed.
Hard to know what the real problem is, but those are some guess of things I've found.