Actually it's false.
While Welfare, WIC, EBT, and whatever else are funded by the Federal Goverment, they are administered by the States. That's money. The more flowing in, the more their economy benefits. Amazingly (I learned this almost a decade ago, verified it, but still can't believe it's a thing) some people, by reporting 2 residences in separate states, collect in BOTH. But all that info in the application down to the Social Security Number? Formalities. Cross referencing? For what, to deprive the state of that additional cash?
There is zero incentive to reduce the rolls at the local level, unless there are cutbacks at the Federal. And given the influence on that from politicians, that tends to be rare or short lived.