You still have an account, even if you have moved to another family. As long as you hold your current ID card, you can open an account in your town to buy social security. Unit social security includes pension, medical care, maternity, unemployment and work-related injury.
If you can't get a medical insurance card, you can cancel the record of the original medical insurance card. Note: it is not for you to cancel your previous social security.
Further reading: How to buy insurance, which is good, and teach you how to avoid these "pits" of insurance.