It is not directly linked. Both are linked to employment (sozialversicherungspflichtig, what atrue German word) which gives you health insurance, social security, unemployment and retirement. Lower salary ranges give you health insurance, but sometimes not unemployment or social security (not sure about the latter without looking it up), while freelancing or being a GM at a company (your own or someone elses) can come without retirement or unemoloyment benefits. Except some extreme edge cases, there is no way to be not health insured in Germany. There are multiple ways to not have unemployment, social security or retirement benefits. The prudent path here is to either contribute voluntarily (expensive with the exception of unemployment) or pick privtar alternatives. None of that so is connected to citizenship so.