You must list all of your creditors in your Chapter 7 Bankruptcy. In bankruptcy you do not get the option to pick and choose creditors that will be included and not included, you must include all of them. The only way to not list a credit card in a bankruptcy is if the credit card has a zero balance (meaning nothing is owed on it, you are not in debt on it).
I understand your concern for your relative’s credit score and the open account. Different banks handle this issue differently. Note that if you do receive a Chapter 7 discharge, you will no longer be liable on the debt on this credit card; however, your co-debtor (your relative) will still be liable for the debt. At that point you will have no legal obligation for paying back that debt, but nothing precludes you from paying back your relative or even the bank for that debt if you should choose to.
As for them closing the account due to bankruptcy, that is up to the bank. Some banks will simply drop the bankrupt person from the account and allow the co-debtor to keep the account, make payments, and make more charges (I know GE Money/Care Credit does this). Other banks will shut down the line of credit.
Overall, as long as your relative makes timely payments on the debt, his or her credit should not be harmed by your bankruptcy.
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(This answer is provided for informational purposes only. Actual legal advice can only be provided in an office consultation by an attorney licensed in your jurisdiction, with experience in the area of law in which your concern lies. This response does not form an attorney-client relationship, nor is it intended to be anything other than the educated opinion of the author. It should not be relied upon as legal advice. The response is based on the limited facts provided. Given additional or different facts, the response would likely change.)
The bankruptcy code requires that all assets and all creditors be scheduled. My colleague's response is well stated.
As for the creditor finding out about the bankruptcy, you can almost count that they will, since most credit card companies review their customer's credit annually, if not more frequently. The BKC file will be right there for all of them to see.
My colleague's response regarding the policy of the credit card companies is also well stated; no need for me to go further.
Not only must you list every debt, but you also must certify that you included every debt. You will be committing perjury if you do not list them all. Once you file, the case becomes public record. Many creditors subscribe to services that notify them once a customer files for bankruptcy, so they will find out. Regarding the account with a co-debtor, I have seen many creditors take the money to pay off the account and then close it. Whether the account stays open depends on the creditor. Many of them will close the account.
[This communication is intended as general information and not specific legal advice, and this communication does not create an attorney-client relationship.]