Depending on the level of basic income, you keep the stick. You just don't beat people to death with it. I don't know about you, but (let's say) $20k/yr wouldn't keep me sitting on the couch. I'd continue to get out bed. That amount, however, might allow someone otherwise unable to do so to go to school, to pursue other interests, to spend more time with their family, and so on. All things that could be long-term more positive than languishing in poverty.
Frugal lifestyles at a modest UBI payout will never know the stick, if the payout is high enough no one will ever know the stick. My point is merely that if the payout allows for a 'basic' income and does as is advertised then there really isn't much of a stick to fear, by some definitions of the 'stick' the 'stick' is eliminated in a scenario where everyone has basic income. Not everyone runs on merely carrots.