The ability to ban or unban a profile from a comment board can be exercised by anyone who possesses the necessary permissions. By default, Comment Moderators and Comment Owners are granted the authority to ban or unban profiles.
If a profile is banned on an application, they will be unable to comment on any comment board and a profile do not lose access to moderation tools if they have that.
A profile with moderation tools can unban himself if its get banned.