This is actually one of the serious problems with the US model of coupling health insurance to employment. When they're decoupled (i.e. employers pay more, employees use those funds to buy health insurance directly from the insurance provider), the damage of losing your job isn't automatically linked to the double whammy of also losing your health insurance (depending on your savings level).
Coupling and single points of failure are a problem in social system design, just as they are in technical systems design.