Between 1967 and 2003, the poverty rate among single mother households fell dramatically, from 51% to 37%. But, on net, for every single mother household that rose out of poverty, 6 new single mother households were formed, of which, 2 now are in poverty. 
Every day in this country, some version of this conversation happens countless times:
“Hey Sam. I’ve got some extra work down at the shop, if you want to come earn some spending money.”
“Sorry, I can’t. I might lose my disability support.”
I don’t point this out to disparage Sam, but to say, what kind of monsters would put Sam in a position where he has to say this?