When a bank fails, the FDIC only guarantees that you will receive insured principal and accrued interest up to the day of closure. If another bank takes over the deposits, that bank is free to not only change the existing CD rates, but to make other changes to the CD terms. However, the new bank must allow you to make a penalty-free early withdrawal. Details of these requirements are described in Dr. Don's answer
to a reader's question at Bankrate.com.
Unfortunately, the article doesn't help answer what are the rights of a CD holder in regards to a changing CD account disclosure by a bank that hasn't failed, as in the case of Darby Direct