It's not basic income if it goes away when you get a job. A large part of the problem that UBI was envisioned to solve is that means-tested welfare systems can

It's not basic income if it goes away when you get a job. A large part of the problem that UBI was envisioned to solve is that means-tested welfare systems can find a steady-state equilibrium as poverty traps (as you noted, if you lose your welfare upon getting a job, the welfare support itself becomes a disincentive to working).