You're thinking like a business not a government/essential service. Unemployment, like a lot of services, could be designed or mandated to break even or turn a profit but whether or not that would work or result in the system failing is another question.

The capacity for a government to run essential services at a loss is a long standing component from even the US founding fathers. Hamilton wanted to adopt all debt from the colonies as a way to consolidate credit, unite the colonies financially, and put stock into the federal government with power to manage the nations debt vs individual states. Jefferson was against the policy but it (and other Hamilton drafted plans like a central bank) were approved through compromise.