I think that either:
1. Most people will be out of a job and will dip into poverty. They'll realize that the .01% have taken all the wealth and will unite against them under the common cause of not starving to death. The .01% obviously can't fight off 99.99% of humanity, even with their robot soldiers, so they go off to space to be taken care of by their machine slaves
2. Same as 1 but the .01% realize 1's inevitability early and go off to space while they still can, leaving the rest of us on Earth to our own devices
3. The .01% give an upgraded UBI to everyone so as to both keep us from revolting and allow us to buy their automation-produced goods