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This seems to be something people don't always give second thought to. When people talk about the homeless, the first things thought about are images of people on busy city streets in rusty clothes waiting around near allies. In there, the answer is quite static, because it can be I guess. But if that's the case, change the setting and that changes too. In the places where I've lived, people often needed that mapped out. Where are they known in your rural locales?
They don't. Winter takes care of that.
On a serious note, there aren't really any in my area. There are some romas during the warmer months, and they live temporarily wherever they can. Usually a small camp in a forest.
If you're a homeless citizen without the means to find housing, you will have housing provided by the local government.
I was about to type this exact thing. We have some homeless of course, people always fall through the cracks - but for the most part, the local government provides for basic needs, shelter, food, money and (in due time) housing. Winter is harsh, you don't really survive living "in the nature" in rural areas.
Summer months often see homeless in the form of "Roma traveling beggars" or the "Irish asphalt/garden workers" who live out of caravans, tents or just back of their cars, but they migrate to southern Europe when winter comes.
But yeah, we pay a fuckton of taxes to have a social security network that catches people who are down on their luck. It's not perfect, but it's something. People don't have to live without food or roof over their heads.
There are homeless shelters here too, but it's not as easy as just making it clear you're homeless. For us, there are so many hoops to jump through that many will feign mental illness to get a "free" stay at the psych ward because it's actually easier.