I'm not sure that I understand your question, but let me give this a try. You are co-signing for a friend so that he/she can obtain credit? If so, then as a co-applicant, you will be equally responsible for the balance, should your friend fail to pay. The creditors can legally come after you if your friend defaults, as you are bound by the terms of the credit card agreement as a co-signer. Your personal information should not print on anyone's report except your own.
If you are obtaining the credit card as the primary and adding your friend as the AU, then you are totally responsible for the debt and your friend has zero obligation to repay the debt. The creditor will come after you, should your friend default to you.
I would suggest not signing as a co-applicant or allowing a friend to be an AU on my account. There exists a high probability that your friend would default [based upon the information that they can not get a secured card] and then you would be responsible for the bill. You will also lose a friend. This is just my opinion. If your friend's credit is that bad, then they need to start rebuilding their credit by first determining the reasons for the denials of a secured credit card and work up from there. Perhaps they lack income, steady employment, whatever. I would suggest that your friend start learning all he/she can about credit and working towards improving their status to be approved for a secured card. JMHO