We have this already: we call it "unemployment insurance".

The government pays you, and you choose what you'd like to do with your time, and the government makes a return on its investment through taxation and the ripple effect. This has been proven to be one of the best ways a government can spend its money when the economy is slumping. The government doesn't even set any limits on what you can do with your time - start any business you wish, not just one in health or energy.