He probably doesn't (and this is a big part of why Papa John's is such a slimy company to work for) qualify for benefits - but then welfare shouldn't be cut.
Despite how much we all rail against the government, they generally don't want to see people starve. They may be inept and have bureaucracy up the yin yang, but there's (mostly) an intention to make sure that people aren't just wasting away.
It just sounds to me like welfare miscalculated her husband's earnings and cut them too much. They are (I believe) supposed to cut welfare payments when someone is working, but not by more than that person's salary.
She can call welfare herself, but it'll light much more of a fire under them if a lawyer does it.