What do you mean by a 'shared' account? If they are merely AU on your account you already know the only sure way to withdraw your permission is to close the account/change the account #. You can then chase your IP's thru perpetuity for help paying the balance. This will have minimal to no impact on your score as the CCC should continue to report you as a cardholder of [x years] standing. Even if it doesn't, unless you need credit right now to buy a car, house or business, keeping the account for the sake of your score is irrelevant - the damage your parents will inflict will far exceed the temporary hit your score might take. If you're really worried, increase the credit limit on a couple of cards before you lower the boom.
If it's a joint account, all the cardholders are jointly and severally liable for the entire balance. The CCC will allow you to take your name 'off' the account only by closing it entirely and paying it off. Then they will report your history for the next 7 years... You (and your IP's) will still be responsible to pay off the balance, but at least they won't be able to add to it.
