What these texts leave out is that the gerundive is often ellipsed:

Interestingly, punctuation can make the difference between a compound sentence and a noun absolute:

The semicolon, a signal of a dump to long-term memory, makes "pointed" in (a) an active, finite verb. But the comma in (b) allows us to read "pointed" as a passive participle ("*having been* pointed"), thereby changing the construction into a noun absolute.

A similar phenomenon occurs in the following sentence, written by a student:
 

At the risk of being repetitious, perhaps I should describe how you should go about identifying noun absolutes. This example is interesting because it is particularly difficult. By the time you get to noun absolutes, you will have been analyzing prepositional phrases, clauses, and even verbals for some time. When you first meet this sentence, therefore, your first task is to analyze everything you can. You might want to underline "reared" as a finite, active verb, but if you do so, you then must note that it is preceded by a comma-splice. Even if you do this, you are still left with three unanalyzed words: "pool," "puffs," and "rising." Your task is to shift through your list of "other constructions" to see if you can use them to explain these words. "Puffs ... rising" is then fairly easily identified as a noun absolute. If you are intelligent, and you are, you should also see that "hood reared" is one likewise. This leaves "pool." How can you explain this noun construction sitting between two noun absolutes? If you use your brain, the pattern is simple: it’s a noun absolute: "a pool of shimmering glass scales *being* around it."

      Most students do not need to be able to make the preceding analysis. The student who wrote the sentence, for example, has an excellent command of syntax -- and a vivid imagination, and most students who use these "other constructions" make few errors with them. I would argue, however, that every teacher of English from seventh grade onward should be able to make the explanation; otherwise s/he might mark the sentence as a comma-splice. [In fact, several teachers have confessed to doing so, and have promised not to so miscorrect students' writing in the future.]

      As a general rule, the noun in a noun absolute comes first, but in some cases, especially with clauses, the gerundive does:

Some teachers will mark this as a dangling modifier, but I can’t see why it should be so considered. Does it not mean:

or, in other words, is it not simply a noun plus gerundive construction?

Noun Absolutes that Function as Nouns

      As adverbs, noun absolutes appear rarely. My research, indicates that Edmund Wilson uses one for every fifty main clauses, E.B. White uses one for every hundred, and Max Beerbohm, E.M Forster, and James Baldwin use less than one in every fifty. But if we turn to their use as nouns, they are more common. Their noun function is obscured, however, because the words can usually be explained in another way. The following sentence is from Max Beerbohm’s "The Top Hat":
 

You could, of course, explain "him" as the object of the preposition "of" and "sitting" as a gerundive modifying it, but such an explanation, although allowable, deflates the nexal connection of "him" and "sitting," a connection that can be seen if we rephrase it to be "portrait in which he is sitting." "Him" and "sitting," in other words, go together first, and then the noun absolute becomes the object of the preposition. 

      I am proud to say that it was a student who first made me pay attention to the noun function of noun absolutes. The class was discussing the sentence:

Someone had already analyzed "windmill" as the direct object of "watched" and "spinning" as a gerundive modifying it, but one student wasn’t satisfied. The sentence, she insisted, doesn’t really mean "We watched the windmill": it means we watched the "windmill spinning": the noun absolute functions as the direct object. Having read Jespersen on nexus, I wasn’t about to tell her that she was wrong. She wasn’t. Note also how close the construction is to the gerund plus subject--"windmill’s spinning." The noun absolute allows us to see the connection between "windmill" and "spinning" as primary, and then to take the entire construction as the direct object of "watched."

For more examples, see the analysis of Shakespeare's 29th sonnet.
See also: Sliding Constructions.

     Although the noun absolute can function as a direct object or object of a preposition, there may be a problem with its functioning as a subject. The following sentence was written by a student:

The writer may have mentally processed "children observing" as a noun absolute, which then agrees with the verb "doesn"t." A reader, however, may process "children" as the subject [which is what I did the first time I read the sentence], and then stumble over the singular "doesn't." Moreover, as the reader gets into the sentence, "children" doesn't make any sense as the subject. To avoid such confusion, perhaps noun absolutes should be avoided as subjects. Replacing them with the gerund -- in this case, "children's observing" -- eliminates the possibility that the reader will process "children" as the subject.