Your family members only become responsible for credit card debt if they're listed on the account.
If they have no ties to the credit card or credit card account then no family members are responsible for your credit card debt after you die.
They will not be obligated to pay off your credit card debt and the credit card company will just have to write the debt off as a loss.
The credit card companies are insured for these types of things when a person dies.
Now if the spouse or other family member jointly owns the credit card account or they have a credit card in their name on your account then yes they'll be responsible for paying back the credit card debt including yours when you die.