Using the Account
When you add a secondary account holder to your account, he can typically use the account as if it were his own. For example, if you have a joint bank account with another individual, the other account holder can withdraw any money that is in the account. He can also deposit money in the account. This gives him free access to use the account, since he is listed as one of the account holders on it.
If you have a secondary account holder on one of your credit cards, it could result in extra debt being accumulated. The secondary account holder can use the account to make purchases as if he were the primary account holder. As long as his name is on the account, he can use the card to make purchases. The secondary account holder can spend until the credit limit on the account is reached, or until you remove him from the account.
Secondary account holders can also negatively impact the primary account holder by losing assets in the account to judgment. For example, if the secondary account holder has an outstanding debt and gets a judgment filed against him, creditors can come after the money in the account. Even though the money in the account may be the primary account holder's, creditors can come after it as long as the secondary account holder is attached to it.
Closing the Account
Although the secondary account holder can typically use the account as if it were his own, he cannot close down the account. To close down a joint account, it will take the consent of the primary account holder. However, the secondary account holder could potentially take all of the money out of the account and simply leave it open instead. Because of this, it is important to evaluate who you list as a secondary account holder.