The two best examples I can think of are Cracker Barrel restaurants (though not so much anymore) and Dan Akroyd’s House of Blues. These places are structurally sound, up to all health and fire codes, and there’s nothing wrong with them, but they are made to resemble ramshackle falling down roadside dives. There’s an ersatz hominess and forced nostalgia to both: it’s almost like a mask in that they’re wanting to imply the structure they’re based on without having its shortcomings.
On the one hand you might be refering to Victorian Eclectic, or Greek or Gothic Revival.
Or, on the other, what Joshua Glenn refers to as “fake authenticity” in Hermenaut. I don’t think though that there’s a good commonly used term. I always fall back on terms like rustic, fake rustic, pretend rustic, etc.
Not so much architecture, but when this sort of effect is applied to items of furniture etc, the style is often referred to as distressed - I see no particular reason why this term couldn’t also be used to describe architecture, but I’m not sure if it commonly is.
Don’t know the name but I went to a restuarant on the other side of the river from New Orleans that looked like a total wreck from the outside but a solid structure quite nice on the inside. Also there is a chain of restaurants (each with different names, like 94th Aero Squadron in College Park, MD) built to look like a WWII air base that was fairly bombed out. Usually built next to small airports.
I was crushed when I recently learned that 94th Aero Squadron in San Diego was part of a chain. Still one of my favorite restaurants, the Sunday brunch is divine.