For security, you will be providing the Cox account 16-digit number, your PIN, or the last four digits of your Social Security number, as well as a secret answer to the secret question. We are always advised to regularly change the passwords to our email accounts to ensure it is secure against all possible attacks and threats on the Internet. By changing our password, we may be making it harder for any potential hackers to access the Cox email account, and therefore, Cox email accounts are kept safe from any possible attempts of threats, which are quite prevalent nowadays. I was told via a cox representative through a live chat, all cox can do is move all the email accounts from one Cox Internet Service Account to another, provided that there is no Primary Email Account created on the new account.
See also - https://www.newsniz.com/cox-email-not-working-on-iphone/