There is an amount of people who own, well, in the past we could say "means of production" but let's not. So, they own the physical capital and AI worker-robots, and this combination produces various goods for human use. So they (the people who own that stuff) trade those goods between each other since nobody owns the full range of production chains.

The people who used to be hired workers? Eh, they still own their ability to work (which is now completely useless in the market economy) and nothing much more so... well, they can go and sleep under the bridge or go extinct or do whatever else peacefully, as long as they don't try to trespass on the private property, sanctity and inviolability of which is obviously crucial for the societal harmony.

So yeah, the global population would probably shrink down to something in the hundreds millions or so in the end, and ironically, the economy may very well end up being self-sustainable and environmentally green and all that nice stuff since it won't have to support the life standards of ~10 billions, although the process of getting there could be quite tumultous.