In the course of establishing a revolutionary society, we will eventually have to deal with an important problem: what do we do with the rich people? Being non-coercive, we don't want to just kill them. And having a respect for personal property (i.e. possession, c.f. private property or capital), we don't just want to dispossess them of all their wealth. But we also want to create an egalitarian society, so surely we can't just let them keep their yachts and mansions and golf courses! ...can we?
Well, let's think this through: is property the extent of wealth? No. Let's see why:
Wealth depends on public power to defend it both from roaming hordes of peasant criminals who might wish to take it by force and the pesky egalitarianism of real democracy — the Founding Fathers of the United States consciously established a state that would defend the rich against the poor. In a real democracy, the accumulation of wealth would be impossible since the poor could just vote to redistribute land and capital; this, in fact, has been the main cry of every peasant revolt in history — cancel the debt and redistribute the land.
Wealth just as crucially depends on something a little more subtle: the private power of the wealthy to command the resources needed to sustain and maintain their property. By this I mean the army of servants, groundskeepers, housekeepers, mechanics, drivers, sailors, caddies, security guards, technicians, etc, that are needed to keep a mansion, yacht, golf cart, kitchen, etc, stocked, operational and convenient. Without the economic power to hire and fire the said army, the lifestyle of the rich becomes impossible for any length of time. Machines break down, houses become decrepit, country clubs grow weeds.
With the rapid or eventual elimination of the State, the public power to defend the rich obviously disappears. But less obviously, with the rise of socialism (that is, the control by workers of their own labor) the private power disappears as well. When workers are not dependent on the workings of financial and labor markets to feed themselves but instead organize work and distribute goods based on principles of mutual aid and the needs of the many, there's no time to do upkeep on the toys of the rich.
The upshot of all this is, a libertarian socialist society doesn't need to do anything with or to rich people. It's almost certain that we'll never really need to commandeer the land that mansions sit on, or the harbors that yachts are docked at (not to mention the mansions and yachts themselves). The rich can keep them, for what they'll be worth with no workers willing to do maintenance on them, or provide them with fuel and food and service besides the basics that anyone would be entitled to. We can let the rich keep everything they can make a reasonable claim to using, and just wait for them to get sick of living in broken-down palaces, with rusting yachts in their rotting docks. No coercion, appropriation or, really, action necessary.
(This of course says nothing of what we do with those things that the rich cannot reasonably claim to use, such as huge tracts of empty land, factories, business places, etc, which can in no way be construed to be personal possessions as they fundamentally depend on the labor of others for their very existence.)
