If we define the noun in some other way, then the relative clause can be either defining or non-defining, depending on the context.
Jack is wearing the hat that is too big for him. (Not the one that is the right size.)
Jack is wearing the hat, which is too big for him. (Only likely if the people talking know exactly which hat is being referred to).
Jack is wearing his hat, which is too big for him. (Jack almost certainly possesses only one hat.)
Jack is wearing his old black hat, which is too big for him.
Yesterday I met the friend that I very seldom see. (There is only one of his friends that the speaker seldom sees.).
Yesterday I met my old friend Jack, who I very seldom see.