What happens to private health insurance companies if American health care is nationalized?

bdunc295 asked:


Few would be willing to dish out for private coverage while they are receiving health care from government taxation. Would the private health industry perhaps dwindle down to a few big players and be forced to take a hit by improving coverage and care?
I'm well aware health care won't be nationalized. I meant to indicate this is a hypothetical question.

Gretchen