Does it say how much money the lawyers charge? Do they expect payment up front? Or do they get money after they process those claims? How much? This almost seems illegal that states are moving people off welfare and pushing them to disability. That is an abuse of the system.
The program states that lawyers get a one-time fee of up to 25% of the backpay.
The biggest law firm in this space, Binder and Binder, got $68M last year from government for ~30,000 cases processed. So it's not a windfall (~$2,250 per case) but if you can do it cheaply enough, the volume makes up for it.
For the firms that help states move people from welfare to disability, they also get ~$2,300 per successful case so that seems to be the going rate.