In "The Minister's Black Veil," Mr. Hooper never actually had a wife. When the story opens he is engaged to a young woman named Elizabeth, and they are deeply in love. She would obviously make an excellent wife for him, but she breaks off their engagement when he informs her that he will never remove his black veil even after they are married and even when they are in bed together. She never marries anyone else and remains devoted to him all her life, although their relationship is strictly platonic. Many years later when he is an old man and still wearing the black veil on his deathbed, Elizabeth is a depicted as acting as his nurse.
Are you referring to "The Minister of the Black Veil" written by Nathaniel Hawthorne? If so, than Mr. Hooper's wife is named Elizabeth. They are actually not husband and wife--she is his fiance (this is what plighted wife refers to). Elizabeth is not fearful of what the veil conceals. She actually ends up breaking the engagement off when Mr. Hooper refuses to unveil his face. She said that if he would have removed the veil, it would dispel any ideas that he is insane or hiding some sort of sinful scandal.