Maybe employees get a vote on who to fire.

well, that's simply not how any business works, even in the most extreme naively theoretical socialistic case. why would a company do that? - employees don't (generally) own the company.

even for some reason they were forced to, in practice, a cadre of employees (most likely the ones you'd want to fire in the first place), would instantly form some new ad-hoc political layer to exercise political power and control the organization, voting, etc.

so you just end up with a layer of useless management and a independent layer of useless politicians, neither of which are willing to fire themselves.