What server? Where is the email hosted? The answer depends on how yu answer those questions.
But really why bother you can ignore any old emails accounts you might have. But before you abandon the account set the password on the account to somethings like 50 random letters and numbers.
Ah, you have an Apple ID then that was migrated from the old system. As far as I know, there's no method Apple exposes to users to completely expunge their accounts. It turns out that I have a similar issue, and I'm in the same boat - I need to call Apple to get it resolved.