I don’t think this is entirely accurate. People who sell their labour for money are all working class… and this would easily cover people right below rich.
Those who start letting money do work for them can be considered the owning/capitalist class.
Now if they are able to stop producing labour because the money they have is generating more money then at that point it becomes a problem because we have arrived at an infinite money machine which is unsustainable in a finite world.