Do low wage employers get subsidized?

So claims a study from UC-Berkeley that was summarized recently by NYT.  It is true that many employees of companies such as McDonalds and Walmart receive some form of public assistance.  But when economists think of subsidies, we usually think of payments designed to encourage production of certain activities, such as higher education and corn.  In other words the more the company produces the more the government pays them!

The situation with low wage employers (large and small) is fundamentally different.  Public assistance programs are designed so that as people work more hours their assistance levels go down.  A low wage worker at McDonalds does not make enough money to be off public assistance, but the public assistance payments are LOWER than if he or she were not employed at all.  How this gets translated into a subsidy is beyond my comprehension.

Nonetheless I find the picture painted in this story very disturbing.  In a well functioning labor market, single mothers in their 30s should have better options than working in fast food or greeting shoppers at Walmart.  Part of the problem is that globalization and technological change have eliminated a lot of jobs.  Another part is that these workers do not have enough skills to qualify for whatever better paying jobs might be available.

How can we devise a way to get these workers the education or applied skill training that would open more opportunities?  I expect more creative use of online learning opportunities could make a difference.  But that does not seem to fit into the platform of either major political party; one seems to want to turn back the clock while the other is under the illusion that markets solve all ills.