If the hypothetical we're discussing is "kill all the rich", assuming the year after takes place in a capitalist economy doesn't seem like a sure thing.

Then construction would increase, causing rents to fall.

What could this mean? For example if some rich person had a few billion in T-bills or Apple stock, when they disappeared what would happen to those? If that ownership just vaporized, the national debt or Apple's shares outstanding would fall. In effect US Citizens or Apple shareholders would be wealthier.

The only other option I can see is that some tiny percentage of the country or of Apple would disappear. But what part, specifically?

This comment to me is characteristic of thinking of ownership in far too simplistic terms. Very rich people don't actually own productive things, they just own rights to income streams.

There are certain exceptions, such as the Koch brothers who do own their companies. If those companies disappeared that would also be a net benefit to US citizens.