A character has no friends but has one person who's closer than everyone else.
Some people have only one friend. Others don't even have that. While the Only Friend is genuinely a friend, the Closest Thing To A Friend genuinely isn't a friend. The reasons for a character having the former are often similar to the latter. Maybe the character lacks social skills or is otherwise unlikable. Maybe he's too emotionally or mentally damaged to form proper friendships. Maybe his chosen profession or lifestyle keeps him from making friends. In some works, this character may graduate to another character's Only Friend.