Wilderness huts are special free shelters in the backcountry, meant for short stay. Although comfort varies, mostly these shelters have at least a fireplace and a place to put an isomattress.
Especially in more populated areas, the shelters are often quite close to a settlement and so within walkable distance from a (main) road.
In Andorra there are 26 mountain shelters. See here.
Throughout the mountainous regions of France you'll find free shelters to use. The website Refuges.info lists most of them. Unfortunately only in French. Select a region and look for Cabane non-gardée.
Here you can see a number of very simple, mostly open shelters in different areas of Germany. Look for articles starting with Schutzhütten to see huts listed with GPS-coordinates.
Slovakia and Czech Republic
The website  has an overview of free shelters in mainly Czech Republic and Slovakia. It also shows some huts in the Alps. Shelters are of different quality and accessibility, but the info is very elaborate. (In Slovakian)
In the Carpathians there are some informal huts one can use. They are marked on 1:50.000 hiking maps of the region.
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