A rumor began circulating among the people that the queen was an ogress and had eaten her own child.
The bold subordinate clause modifies "a rumor", but is this considered extraposition? Normally, extraposition involves a dummy pronoun as the subject.
- [A rumor that the queen was an ogress and had eaten her own child] began circulating among the people.
- [A rumour] began circulating among the people [that the queen was an ogress and had eaten her own child].
In sentence (1) above, we see the long noun phrase (NP for short) in brackets appearing as Subject of the clause. It contains a smaller content clause: that the queen was an ogress and had eaten her own child. This clause is the complement of the noun rumour. Notice that it appears after the Head noun, rumour. We can often place modifiers and complements that usually occur after the Head noun at the end of the clause if they are long. This is what we see in sentence (2), where the content clause is not part of the Subject, but occurs at the end of the clause instead. This is usually called extraposition from NP. The word extrapose, of course means to put outside. Here we see that the content clause no longer occurs within the NP and has been "put outside" the nucleus of the clause.
- [That the queen was an ogress and had eaten her own child] was clearly nonsense.
- It was clearly nonsense [that the queen was an ogress and had eaten her own child].
In sentence (3) above, we see a content clause functioning as Subject of the sentence. We don't like to use long clauses as Subjects in English. We prefer to use a dummy pronoun, it as the Subject of the clause, and to move the content clause to the end of the sentence. This is what we see in example (4). This type of construction is usually referred to as an extraposition. Notice that this is different from what happened in sentences (1) and (2). This time the whole of the Subject in (3) appears at the end of the clause in (4), not just part of it.
The Original Poster's question
Normally, when people talk about extrapositions they are talking about sentences like (4) which use a meaningless pronoun, it, to fill some syntactic position in the sentence. However, people also talk about extraposition from NP to refer to the phenomenon we see in (2). Occasionally, in the right context they may abbreviate this to extraposition.
Because it is clearly very easy to confuse these different types of construction, some modern scholars, for example the authors of The Cambridge Grammar of the English Language reserve the term extraposition to refer to sentences like (4) above. They use the term postpose with regard to sentences like (2). They would say with regard to that sentence that "the complement of the noun rumour has been postposed". This avoids a lot of confusion!
A rumor began circulating among the people that the queen was an ogress and had eaten her own child.
No, this not an extraposition construction. The expression in bold is a postposed content clause functioning as complement (not modifier) of "rumor".
The content clause would normally be integrated into the structure of the noun phrase, in this case occurring immediately after the noun "rumour":
A rumour that the queen was an ogress and had eaten her own child began circulating among the people.
You are right that in subject extraposition the subject is normally the dummy pronoun "it" as in, for example, It horrified her that the queen was an ogress and had eaten her own child, where the basic (non-extraposed) version would be That the queen was an ogress and had eaten her own child horrified her.
