Depends where in Europe. In Germany, if you lose your job you still have to pay for health insurance, at least the first three months until your unemployment kicks in (assuming you're eligible for it, like in most cases) and I don't know if unemployment covers your health insurance.
If you are married and you and your spouse were on the same statutory health insurance, then you're covered by your spouse. Which can be the case in the US depending on your spouse's coverage.