We all should pay for the worker's social safety net. That shouldn't be dependant on a worker's employer, or even employment status. In the US, tying health insurance to employers was one of the worst public policy mistakes we ever made.
Not only is it tied to employers, it's subsidized! If a company gives you $1 in salary you pay taxes on that dollar. If it gives you $1 of health insurance it's tax free. It's madness.