Unemployment is first funded by the employer (in some states a tiny percentage comes from workers), which is why one has to hold a job for x weeks before being eligible. But benefits are limited and any extension of unemployment benefits is funded by the government’s money tree (the taxpayer).
I consider “funded by the employer” the equivalent of “funded by the worker,” since anything the employer pays the government *doesn’t* go to the employee.
That is to say, you’re right, but I’m quibbling ;-).