In my mind, I still think 100% unemployment would mean a lot of people who live today in relative comfort, and are therefore complacent with oligarchy, would get very mad. Even if bought by billionaires, I doubt they'd retain the same quality of life as when the economy needed them.
And I don't see billionaires isolating themselves forever in gated communities, what's the point of being this powerful if you live in a golden cage? Look at Musk, he's the richest man in the world, and could just chill in the shadows but is constantly seeking attention and recognition.
My prediction if we get there is that the "AI" will present us with a seemingly 'benevolent' solution.
"AI has solved everything. Climate change. Limited resources. AI can fix it all. Everyone except a select few must stop ... reproducing."
It's like when a large organization wants to reduce headcount and they do it with buyout packages and retirement.
The billionaires can always do what they've always done and pay half the poor people to shoot and oppress the other half if things don't go their way. As long as you keep the people with guns well paid, you're good.
Dividing the lower classes and pitting them against each other has always been successful in conquering them and preventing them from uniting and rising up again the ruling elite because collectively, people are stupid and easy to manipulate against their own interests, like cattle.