We had a situation where a client was trying to log out of an old Apple ID, but the password was not accepted and when we selected Forgot Password, Apple said the email address was not a valid Apple ID. We needed to log out of the incorrect Apple ID in order to log in to the client’s current Apple ID.
Solution: We turned off the wifi connection on the computer and then chose Log Out. We were able to log out of the incorrect Apple ID.
When you use this method, you will not be prompted to save any information in iCloud on your computer. Please make sure your information is all stored on your computer before you choose Delete and Disable.