Way back in the 60s there was a system proposed called NIT (Negative Income Tax).
The idea was that everyone would get the absolute minimum necessary to live but they could earn more by working with the NIT reducing by a percentage of their earnings.
The only real problem with that was the fact that all the welfare departments and organisations would be replaced by the income tax department - you filled in your tax forms and they worked everything out.
If I remember correctly it got talked about in the UK House of Lords and some actual tests of the system were carried out in the US (a few selected cities).
I think the main reason it wasn't adopted was that it would put too many peoples noses out of joint because they saw it as something for nothing ignoring the fact it mainly replaced the welfare and/or unemployment benefits that were available.