Many verbs take finite clauses as Complements, often introduced by the subordinator that:
- I know [that elephants like donuts]
- I said [that elephants like donuts]
- We allege [that elephants have been eating our donuts]
Many nouns can take finite clauses as Complements too:
- The idea [that elephants like donuts] is not new.
- The news [that elephants like donuts] is spreading like wildfire.
- The insinuation [that us elephants have been eating your donuts] is unwelcome.
Sometimes, especially if the clause is very long, it can break away from the noun and move to the end of the clause:
- The news is spreading like wildfire [that elephants like donuts].
These types of finite clauses that appear as the Complements of nouns and verbs are referred to as content clauses by sources such as the Cambridge Grammar of the English Language.
Now, noun phrases which take content clauses look a bit like nouns being modified by relative clauses (a relative clause is a technical term for an adjective clause). Here are some nouns that genuinely are being modified by relative clauses:
- The news [that is spreading like wildfire] has astounded elephants everywhere.
- That idea [that I got from the internet] has proved very popular.
- The insinuation [that you made] was most unwelcome.
- The news [that he'd been waiting for] arrived.
Now sometimes, for example if we have an intransitive verb and a long relative clause, relative clauses can also break off and move to the end of the sentence:
- The news arrived that he'd been waiting for.
Distinguishing content clauses and relative clauses
Now there are different ways to try to understand whether a clause is a content clause or a relative clause (adjective clause). If the clause is a content clause, it will be grammatically complete in the sense that all the material after the word that will work as a stand alone sentence. So for example, in "the news that England had won the world cup", the material after that will work as a stand alone sentence:
- England had won the world cup.
We can contrast this with "the news that he'd been waiting for" from one of the relative clause examples:
- *He'd been waiting for. (ungrammatical)
Here there is a gap after the word for which we understand as representing the news. We can represent the sentence like this:
- The news that [he'd been waiting for
However, it isn't always so simple to see where the gap in a relative clause actually is. A better way to see what kind of clause is involved is to see if you can change the word that. The word that can nearly always be substituted by which or who when it occurs in a relative clause modifying a noun. However, the subordinator that which we find in content clauses cannot be substituted with a relative wh- word. Consider the following examples:
- The news which he'd been waiting for arrived. (grammatical - because relative clause)
- The news which elephants like donuts is spreading like wildfire. (ungrammatical - because content clause).
The Original Poster's example
A rumor circulated among the staff that he was being promoted to Vice President.
In this sentence the clause that he was being promoted to Vice President has broken away from the head of the noun phrase a rumour. As reconstruted by the Original Poster, the canonical phrase order would be:
- A rumor that he was being promoted to Vice President circulated among the staff
Here the main verb in the sentence (the matrix verb) is the word circulated. All the material before the verb constitutes one long noun phrase functioning as Subject of the sentence. The clause following rumour has its own verb. We can show that this is a content clause and not a relative clause by substituting the word which for the word that:
- *A rumor which he was being promoted to Vice President circulated among the staff. (ungrammatical)
Notes for grammar junkies
The phenomenon where the material after the noun in an NP breaks away and drifts to the end of the clause is known as extraposition from noun phrase movement or extraposition from NP for short. It usually only happens if the element is quite long.