Banks can close member accounts for different reasons. Sometimes this can happen due to an identity theft, in other cases accounts are closed due to bad credit or a lack of payment on money owed to the bank. It is usually possible to reopen an account in these cases, but can be difficult depending on the specific circumstances.
In the event of an identity theft, banks reserve the right to close an individual bank account if they have reason to believe that it has been compromised. Wells Fargo and Bank of America have provisions that allow for these accounts to be reopened, but they require the account number to be changed, as well as for the owner to establish new passwords.
An account due to failed or late payments or bad credit is a very different circumstance. The decision to close, as well as whether to allow the reopening of an account in this case, is basically at the sole discretion of the bank. It is up to the individual whose account was closed to not only pay the bank back for the money owed in full, but also provide some level of proof of income. This will assure the bank that no further credit issues will persist, and improve the chances for the reopening of the account.