My corporation is paid by another corporation who hires me. They don’t pay unemployment because I’m not their employee.
I’m employed by a corporation I own. Therefore, I “pay in” out of my own pocket when my corporation pays me a salary.
So in the scenario you describe, you are not actually unemployed. Analogous situations would be a law firm with no clients, a dentist with no customers, etc… You would only become unemployed if the corporation you own lays you, the employee, off. Unlikely to happen, but not unheard of. Perhaps your company grows, you hire some employees to take over your tasks, and you no longer require your services. At that point, the corporation could lay you off, you could collect unemployment, and — wait for it — you would still get your distribution if the company is profitable.