I posted an answer in which I rejected your premise. Now let me post an entirely different answer in which -- for the sake of argument at least -- I accept your premise.
What happens to the unemployed people?
One: They starve.
Two: There is some mechanism to provide them with a decent life. The government or private charities gives them money or provides free food and housing or something.
Three: There aren't huge numbers of unemployed people, but rather everybody becomes partially employed. Maybe the average person works only 5 or 10 hours a week and that provides all the income they need for a comfortable life.
Three sounds great, but given the premise may be the least likely. If robots are doing all the menial jobs so that all that's left are the jobs that require special skills that the robots are not (yet) advanced enough to do, than people who DON'T have management ability, or technical skills, or creativity, may be unemployable.
So what do the unemployed do with their time?
One: Creative things, like writing and producing art and music and inventing. Okay, arguably this is productive work, but the sort that machines are least likely to be able to do. You may or may not get money for it.
Two: Improve yourself, so that you can become employable. If only people with creative or technical skills can get jobs, than learn to be creative or technical.
Three: Improve yourself, not for the sake of being able to perform some job, but for its own sake. Study history or philosophy or science or whatever. Travel. Visit museums. Get together with friends and discuss great ideas.
Four: Have a good time. Go to parties, concerts, and movies (or holoshows or whatever they have). Maybe this includes drinking and drugs and wild sex.
Five: Join a gang. Spend your time beating people up, stealing and vandalizing, and fighting other gangs.
Of course people could do some combination of the above.
Realistically, some people just aren't capable of doing creative or technical work. Large numbers just won't be able to do One or Two.
Many people would be bored by the idea of a life of endless study. People would probably talk about it as a good and worthy thing to do, but relatively few would actually do it. Like dieting and exercise.
That leaves partying and crime. I suspect that's what most of the unemployed would do.
Okay, it didn't take a lot of deep thought to come up with this list. It's pretty much what unemployed people in our society do, just multiplied.
I've read books that imagine machines doing all the work and that paint a utopia where the people spend all their time producing great art and science. Bosh. Some would, but most just wouldn't have the inclination or the ability. The reality is, for most people, if they didn't have to work, they'd spend their time lying around doing nothing, partying, and/or fighting.
At the other extreme, I've read books that imagine machines doing all the work and that paint a nightmare world of unemployment and starvation, with a small elite living in luxury. Also unlikely. Human nature being what it is, sure, there will be some of the rich and powerful who say to let them starve, but there will be some who care and look for ways to provide for these people. Throughout history there have always been greedy and selfish people, but there have also been people who devote their lives to helping the poor and weak. Furthermore, massive numbers of desperate people makes for a very unstable social situation. The rich would be in constant fear of riots. Even those who care only for themselves would likely see the solution as some combination of strict law enforcement and enough charity so these people aren't TOO desperate, so that they have something to lose if they challenge the system.
If the society is really so rich -- I mean the robots are producing so much wealth -- that there is just no need for people to work, then presumably there is enough abundance to let the unemployed have at least a basic, decent living.
Reminds me: According to the Bible, the law in ancient Israel was that when a farmer harvested his crop, he was supposed to leave a little behind, and the poor were then allowed to collect this. So the rich provided food to the poor, but the poor still had to go to some effort to collect it, nobody brought it to their door. Perhaps in a society such as you propose, factories would have places where they'd dump their slightly imperfect items, or some percentage of their production, and the poor could come and take it.