Prime at what point is it the individuals responsibility to find full time employment that pays a decent wage?
From the start. If they need fulltime work to make ends meet, it is their responsibility to seek it. Unfortunately, seeking and finding in today's market are not always synonymous. Have you never taken a stopgap job until you could find something better? Sometimes and for some people these stopgap jobs trap them into years of underemployment.
This doesn't always happen at the onset of seeking for employment. People in the middle or latter part of their working lives are sometimes laid off for a variety of reasons. I know, I've been there. My position was contracted out to a private company when I was 50 years old. While I wasn't laid off, I was put in a position of having to decide between taking a lesser position or quit. I chose to remain employed with the same company. My wages were subsequently frozen for 10 years before I saw another increase in salary. Incidentally, I did seek other employment, but was unsuccessful. No doubt being in my 50's and having a higher salary requirement then someone at the entry level was something of a determent for me. It's a common situation, unfortunately.
I knew of a longtime factory worker for Bingham Willamette in Portland. His position was eliminated when they moved their operation to a third world country and when he was near the end of his working years. He ended up working for a Seven Eleven to pay the bills. Life can be the shits sometimes and those of us who survive often do so because we make sacrifices or compromises we never thought we'd be making.
Imagine some young person just starting out who has a family to support and little or no skills. They pretty much are stuck taking whatever employment they can find. It is not that this is anyone else's fault or responsibility, it just is and it is far too common. If I were the CEO of Walmart, I guess I would say thank goodness for these poor suckers, because they are making me and the company shareholders rich.