How come people keep repeating that ... and yet ...
https://www.youtube.com/watch?v=LCg9htpWf0A
For example. A few searches yields plenty of recent movies about large amounts of homeless. But more specifically, if you go to Amsterdam, Brussels or Paris by train you will have no trouble whatsoever finding lots of homeless people. Granted, Amsterdam has a few, Brussels a pretty sizeable lot and Paris has tens of thousands at least.
In each of those cities, by the way, homeless are persecuted by the local police, and nothing ever seems to make any difference. Knowing the inclination of Dutch people (protestant, or to put it more bluntly "it's their own fault, obviously"), I don't envy the Dutch ones.
And whilst the poor people in the Netherlands live in extremely shabby apartment blocks riddled with crime rather than trailer parks, other than that there is little difference : garbage everywhere. Many youth gangs that have no option but to turn to crime and prey on their own community. Immigrants being the large majority of those people.
Oh and if you talk to them you will immediately find out, especially in the Netherlands : if you actually use the social safety net, you have to submit to the government "running your life". That "help" the government provides seems to have more than a few people who abuse the power they have (to, for instance, take away child care, or any children, require you to undergo psychological internment or take away your unemployment insurance). There's no end of complaints about that, especially in the Netherlands (less, but certainly present in Brussels and less in Paris).
Brussels and paris have homeless tent cities (maybe Amsterdam has them too, I don't know. Not in the inner city it seems. Both brussels and Paris have them in the inner city.
So there seem to be plenty of ways to "fall through" the social safety net in Europe. And this is the situation in the richest, most prosperous parts of Europe. There can be little doubt that the situation in Romania, for example, is far worse.