One solution to the problem of unemployment is for the state to hire everyone at minimum wage. Everyone else that wants a job done will have to pay more than that, and will not dare to steal workers' wages.

I am not sure how to deal with unauthorized immigrants, though. If the program hires them, people from around the world will try to pour into the country, overloading it. But if the program doesn't hire them, they will be easy for employers to exploit, which will undermine the intended effect.