The implication of your comment is that people only do productive work now because they are forced to, to avoid starvation. And that you think such a system is fine. Because if you thought people now do work which interests them, you'd still think that in a UBI world, and if you thought the current system wasn't fine, you wouldn't go straight to "but who can be forced to do horrible things if we take the forcing lever away? That would be bad".
This is not about being productive. Productivity on its own is meaningless - when I draw I can work really hard but the effects of my work are literally wothless from the point of view of society.
I believe that capitalism works only because people need incetives that are aligned with society needs. Otherwise they will work really hard on stuff that uses resources but will not be part of sustainable system.
Probably people that "want more" than whatever the government stipend buys them. I would probably change nothing about my day to day if I the government started paying my living expenses, except worrying less about what happens if I become unable to work.
UBI probably won't pay enough to have high-speed internet in a two bedroom apartment in a popular city center eating at fancy restaurants three meals a day. It will be the absolute minimum to not die if you can't work. So, people will probably go to work to have a better life than that, but at least have something to fall back on if it doesn't work out. Having a fallback means startups, volunteering, self-care, all sorts of good things. The risk of starving to death living in a cardboard box goes to zero, which prevents a lot of people from doing a lot of things. It's a very real possibility in the current world.
I think people that read this site don't quite understand what "real life" is like in America. There are no paid sick days. If you don't report to your shift, you're fired. If you're lucky, you very carefully fill out the right paperwork and keep your job this time as a courtesy. (There is no federal protection here; for example, FMLA doesn't apply during your first year or so at a job. Some states do a little better, but with remote work, you'll find that most of the jobs are in states without protections! Happened to a friend, though their home state also offers no protections.) While you're sick, you still have to pay for rent and food. UBI is the acceptance that corporate America isn't going to cover routine events like receiving medical treatment. It won't enable people to party 24/7 for 80 years on the taxpayers' dime. It just means you don't starve to death if you get unlucky.
People will continue working to do a little better than merely existing, if they're able.
The robots. The concept of UBI is precipitated on the idea that the gains from technological innovation have been unequally distributed since the founding of the country. It has just been getting to the point where it is very evident to many people now.
In fact Thomas Paine wrote:
"To understand what the state of society ought to be, it is necessary to have some idea of the natural and primitive state of man; such as it is at this day among the Indians of North America. There is not, in that state, any of those spectacles of human misery which poverty and want present to our eyes in all the towns and streets in Europe,"
The real secret is to be the guy who can fix the robots - the new blue collar. Doesn't matter which way the world turns out - either way you're living comfortably and coasting below the radar.
Private equity will own the robots. UBI is not all roses. It will be a way to give the masses a way to live their lives with a minimum amount of dignity and prevent a complete revolt once all jobs are gone through no fault of the people. This will likely also close off the remaining avenues to escape the lower middle class into upper classes. Whoever acquired capital early on wins and everyone else is stuck like in the centuries past. Think about it. Most of the 'new' billionaires are from tech which was an odd fork in history that the old elite clearly didn't see coming. Now the new rich will be pulling that ladder up from behind them once the robots do every job and UBI gives you a bread and circus.
Until they build a robot to fix robots. The real secret is to be the guy who designs robots, because robot designer will be the absolute last job to be automated :P
I presume the same people doing productive work today. I think it would be a great net positive if all the people who want to sit around and do nothing all day would just go and finally do that, rather than getting in my way all the time at work.
Maybe not people doing "productive" work, but the people who pay most of the UBI would possibly the billionaires and corporations who have dodged taxes since their conception.