People continue to work after they have enough money not to; people making $40K per year go to night school to try to increase their income.
Most people continue to want more after their basic needs are met.
And beyond money, work can give a sense of purpose and a connection to other people.
The promise of UBI is saving money and unlocking more human potential (by allowing more risk taking, or letting artists pursue their art, or whatever). But if you think of the need to be productive (for survival) as a force/pressure that has shaped the complex system we call society since the dawn of civilisation, then I can imagine that removing that force in a large nation could result in something extremely dysfunctional or even horrifying.
That's why UBI is only now becoming a possibility.
The need for everyone to be productive is diminishing. The labor force participation rate has dropped enormously since 2000.
(of course a slow implementation would have to overlap with existing benefits, not replace them)
The people who are likely to drop out of their job are plumbers, dishwashers, garbage collectors, miners, mail carriers, highway maintainers, taxi drivers, manual fruit pickers and the rest of those performing soul-crushing jobs that actually allow society to keep running.
Same thing for any other currently low value jobs. We will have to adjust to paying people properly, even above minimum wage, to do things that suck. I view this as a desirable outcome when considered against the current situation in which only the most glamorous jobs tend to pay well, even if the job is not necessarily most helpful.
If your workers are willing and able to do twice as much work in the same time for twice as much pay, you should likely make that switch anyway - at the least it'd save you bookkeeping, and it would be a better use of the workers' time.
And if people systematically decide that they have better things to do than a particular job, and we automate that job so we don't need people doing it, that seems like a win to me.
Whether it means less people working overall depends on how big these effects are, what the effects are on demand, and whether we couple it with other changes like a decreased minimum wage (which could lead to more people working on things which are more pleasant/fulfilling but less highly paid).