So, to make working a second job "worth the jump" it needed to bring in $5k+ more, which very few jobs do on the outset.
Every meal involves a multi-hour line. Every shelter bed too. Every free clinic, etc etc, you get the point.
The net effect is, despite having well-funded charities providing for their basic needs, they have neither the time nor the bandwidth to make any substantial improvement in the long run.
Contrast this situation to transitional homes, where once admitted people are guaranteed shelter, clothing, and food for a period of time, where (basically) the same services are provided but without the daily time sink, and the success rates are much higher (this of course, should account for the fact that transitional homes mostly exclude those who still have major mental health or substance abuse problems).
Both institutions are a source of "free money", but one works a hell of a lot better, largely because it frees them up for higher-order goals.
It would be cheaper to just give everyone free money. In fact, that's the basis of the the various Guaranteed Minimum Income ideas that have been floating around for the past 45 years or so.
I'm pretty sure fewer people die of malnutrition and more people can eat better food as a result of welfare. I'm pretty sure more people have the ability to keep a roof over their heads because of welfare, too.
Given the current unemployment rates it also seems odd that we'd want to predicate the "success" of welfare on whether it is able to make even more people join the workforce.
There are, of course, many flaws with the system. But asserting that it doesn't work doesn't advance discourse in any meaningful way.