How to really deactivate an @mac.com address?

Hello,

I’ve removed an @mac.com email address through system preferences>internet accounts>remove. I now can’t login to that email address anymore. Says it doesn’t exist. I then created a new icloud account with a different email address.

However, if I send an email to my should-be closed mac mail address from another email account, I don’t get an ‘undeliverable’ message back, but still an autoreply I once set for this mac email address. So this means the account hasn’t really been closed. How to do that? Thanks, Marina