"That's a good point. But I wouldn't assume that State funding covers the whole cost of the workers. In addition to payroll, the cost of pensions, benefits, office space, elevator service, payroll processing, HR, etc. might well have been left to the City."

The city may have absorbed some of those costs. The budget doc jt1 linked to doesn't include a breakdown to that detail. But even if that's true, it's only a few hundred employees. The city's going to have to cut a lot more than that to make any appreciable dent in its budget problems.