It's either: 1) the rich voluntarily share the means of production so everyone becomes equal, 2) the poor stage successful revolutions so they gain access to the means of production and everyone becomes equal, 3) the poor starve or are otherwise eliminated, and the survivors will be equal.
All roads lead to equality when the value of labour becomes 0 due to 100% automation.
If truly 100% automation (including infantry/police) the most likely scenario is not any if the above; most people will be kept on some kind of minimum sustenance enough to keep them from rebelling (“UBI”) and those who disagree will either be coopted into the elite or eliminated.
> 2) the poor stage successful revolutions so they gain access to the means of production and everyone becomes equal
Or a handful of the poor become the new rich, which is usually what happens in that scenario.
There's plenty of outcomes besides those three.
Over history, lots of underclasses have been stuck that way for multiple generations, even without the assistance of a robot workforce that can replace them economically.
Some future rich class so empowered would be quite capable of treating the poor like most today treat pets. Fed and housed, but mostly neutered and the rest going through multiple generations of selective inbreeding for traits the owners deem interesting.