The correct option is B That she still believes the person who betrayed her- subject
A noun clause is a dependent clause that functions as a noun. It usually
begins with what, whatever, whom, that, how, why, whether, which and so on. A noun clause can act as a subject, object, predicate
nominative or object of a preposition, in a sentence.
The noun clause
"That she still believes the person who betrayed her" functions as the subject of the verb
"is" in the given sentence.
A that-clause can function as a noun; it can be the subject or object of a verb. It contains a pronoun 'that', a subject 'she' and a verb 'believes'; hence it is the noun clause here. Hence option D is correct.
Option A is incorrect because it is a fragment of the subject.
Option B is incorrect because 'the person who betrayed her' is the object in the noun clause, it isn't the noun clause itself.
Option C is incorrect because it isn't the noun clause nor does it function as the object; it contains a fragment of the noun clause and this sentence does not have an object. ('Unbelievable' is an adjective, not the object of the verb 'is'.)