It's a bit more nuanced than that.
It's not anybody's problem but yours if you haven't put in the work, shown ambition, and taken advantages of opportunities that have come your way.
But it is everybody's fault (meaning, society) if you have never had any opportunities come your way at all, or been given the same baseline advantages that others that came before you have.
For example, Trump likes to spout that he's a self made man (as an example). But he's not - he was literally a millionaire by the time he was 8. That's not hard work, that's the luck of the draw.
The rapidly widening gulf between the very rich and the very poor means that the middle class is vanishing, along with it the very baseline of opportunity afforded to previous generations. If you're born poor in a bad community, for example, your best opportunity might be a minimum wage, part time, service job... and that might be as lucky as you'll ever get.
We are moving rapidly back to a feudal state - nobility and serfdom.
I came from a bad community. I grew up poor. I had that part time service job. I just did it without expenses. I lived homeless for a few years and saved my money. I worked 16 hours a day for two years. It was two 8 hour shifts, with 4 hours off in between each shift. So I got four hours to sleep, if I could sleep. I usually slept in my car at night and on a couch in the break room during the day.
For the first year of this, I would drive home and do chores. And my mother would fly into a rage and throw anything and everything at me.
I felt incredibly rebellious the first time I didnt come home to do chores. I was angry, and I felt like I was doing something wrong. I built a simple shelter at the edge of the corn fields that the university of florida grew for feeding their cows.
Back then, I did a lot of research into niche markets. I sold leaves and oak bark to people who keep fish and wanted a natural looking "black water" fish tank. I sold muscodine vines to people who wanted to use them as non-toxic perches for their birds.
And I worked. I also sold animals to people who wanted them.
I even sold hair algae to people who breed fish, because it boosted their survival rates.
There will always be a way to boost your status and make more money. Most people aren't willing to do it.