Background: Nearly all low-wage labor is done by humanoid robots (retail, factories, transport, sanitation, construction, mining, and similar fields). These robots have all the physical capabilities of humans and more, but jobs that require ingenuity and adaptation such as design, management, etc are still done by humans, and technology allowing robots to fill these jobs is millennia away. 

Problem: Housing, sustenance, and other necessities of life are not free or subsidized and members of society still need to work for these in some way. With menial low-wage jobs being taken by robots, there's no longer a low entry point into the job market, and the design/management/etc professions that aren't filled by robots require advanced training that is not available to the poorer portions of society. How would the population have adapted to allow robots to do low-wage labor? Would all of these people have died off or moved elsewhere? Would society have naturally create large numbers of jobs that require ingenuity but little training? If so, what would these jobs be?

Society is still functioning at this point, and there's a government and workers' rights groups, so Matrix-esque human farming and similar things are out of the question.

Edit: This is not a duplicate of [this question](https://worldbuilding.stackexchange.com/questions/38603/what-would-the-transition-to-a-jobless-society-look-like). The linked question concerns removing humans from the workforce entirely and a money-free society. The aim of this question is human adaptation to a society where money is still present and robots only occupy low-wage labor, and jobs that require ingenuity are still done by humans as initially mentioned in the first paragraph.