Most do not. I was a WA State employee for almost a decade and had to pay for everything. Up to $250 a month. So we paid just like everyone else. A very small % still have everything paid.
Now, there are states like CA and NY where some union employees do get paid benefits. But that is dwindling, even among NYC workers. The CA budget crisis is coming too and something has to break.
Even at Boeing, my neighbors had to begin paying for their own benefits (those hired after certain dates). Those w/longevity were grandfathered (according to my neighbors).