There hasn't been a "Welfare" program in some time, at least by that name.
Instead a bunch of programs have taken the place of welfare. Research these:
SSI
TANF
FI (Family Independence), which promotes DEpendence
SNAP
Plus there are programs to help pay your rent, your utility bill, for daycare, etc. ad nauseam.
And, as you might expect, every program is abused and filled with fraud.
In my state the current manifestation is referred to alternately as "cash assistance" or TANF, depending on where you look on the DSHS website.
I am familiar with the others except for "FI". So I looked it up and here it is (was) referred to as "FIP".
A little summary I found:
The Washington State Family Independence Program (FIP) is a welfare reform program designed to help families become more economically self-sufficient. It was expected to increase participation in education, training, and employment, which would in turn reduce welfare participation. However, relative to traditional welfare, FIP had little or no impact on education and training, it reduced employment and earnings a little, and it increased welfare participation substantially. The authors present data gathered by the Urban Institute over five years and analyze the reasons for FIP's failure to meet its original goals.