Did you deleted iCloud mail account from system preferences > internet accounts only or deleted the other mail account ( like gmail account ) .
Some queries - what is the version of your Mac , the Apple ID account is created with secondary authentication account ( in which three answers for security questions , date of birth , rescue mail address is added ) or the account is associated with two factor authentication .
The Apple ID that you deleted is what ( a ) example1@icloud.com
Have you set up iCloud Keychain , do you know the six digit iCloud verification code , your correct apple id and password ( that you deleted ) , do you use any VPN services , any anti virus , cleaners / softwares , unknown apps in Mac ?And which associated files are deleted from system library or user library and from which folders and where are they have you emptied the trash and why were they deleted ?