The reason why a lot not all, but definitely a notable amount, of even decent, hard working folk, stay poor, is because the minute you earn more than you would receive by simply subsisting on welfare, you are actually losing more money than you gain. There are other effects that are often not accounted for. Like the fact that they make you try to find jobs, and they have to be new ones, a quota of them, regardless of your locations or circumstance. Even if you are a child. Even if there is maybe three jobs in the area that do not require you to travel over a hundred kilometres. Even if they know you do not own a car, they tell you that they will cut off your benefits if you do not 'walk'. Some parts of life, especially for the truly poor, which most people have absolutely no conceptualisation of, who they relate to with almsot no understanding of, the Underclass as it is sometimes called, the <10% or close to, is truly crushing.
You often are in a situation where you have such limited experience, such limited skill, such limited fortune, that you have to take any job that you can, even if the hours are unrealistic, even if you have to travel hours a day for it, even if it actually starts costing more for fuel, than you get paid. Simply because if you do not, you will lose your benefits, and you will go from having less of the benefits than you should, and not even earning any more, to having nothing at all.
You must also consider how it feels to be that person who cannot afford clothes and to wash themselves, and has been rejected or not even applicable to most of the jobs they have found, and has been trying to get ahead, only to realise any move forward will actually only keep them permanently fixed at square one. It is pretty hard not to give up. It is pretty hard not to feel completely abandoned by society. It is pretty hard not to lie in filing reports, not to use specific mechanics of welfare to make it so you barely have to do anything, so you can just rot, and survive. And this is assuming you somehow got a house. Because remember, you do not get welfare deposits unless you have a fixed address. Good luck with that when you are sixteen. Good luck ever building to that point when you started at sixteen. It is pretty hard to not just go sit under a bridge and drink until your organs collapse.
There are still ways out, there are ways to try, though, their success is not guaranteed. But sometimes people just do not know. Sometimes people are well and truly too depressed to possibly even consider it. There are so many things that go into it. One simply has to have a much more open, empathetic mind to it.
Might respond to the other stuff late