I have a campaing and one player claimed a character, but he lost his account, (he states that it does not exist anymore, as he didn't verify it fast enough, or something). I would like to be able to provide the character to be reassignable again.

I want the character to be claimable by a new player (really is the same player but with different account). Remove character from campaign does not fix this.

Why should I do to fix this?

The only user that can unassign a character is the owner of that character.

What I would recommend is for the user to open a support ticket in order to get access to their original account.