The credit card emergency contact is not responsible.
Applying for a credit card is a contract between the card owner and the bank. The contract is only valid for both parties, and the emergency contact person does not have to bear responsibility. The bank can only call and ask the emergency contact to help find the card owner, but repayment is the card owner's responsibility and will not affect the emergency contact's creditworthiness and other records.
Nowadays, credit cards generally do not require a guarantor. When banks find that the credit card is risky and the card owner cannot be contacted, they can contact the emergency contact person.