One result of the alternative shown in [2] is that possible neutralization of the formal difference.

[diamondcutter]

The manager APPROACHED us, SMILING. [1]
The manager approached us SMILING. [2]
One result of the alternative shown in [2] is that possible neutralization of the formal difference between nonfinite clauses functioning as supplementive clauses and those functioning as complementation of the verb.
Source: A Comprehensive Grammar of the English Language by Randolph Quirk, Sidney Greenbaum, Geoffrey Leech.

This sentence is also difficult to understand. Does it mean this?
[2] is ambiguous because the implied subject of the participle “smiling” can be “the manager” or “us”. If the implied subject is “the manager”, the participle “smiling” functions as a supplementive clause and if the implied subject is “us”, the participle “smiling” functions as complementation of the verb “approached”.

 

[jutfrank]

The writer means that since he can't identify any important semantic difference between the two forms, there's reason to think that the formal difference between such non-finite clauses functioning as supplements and those functioning as complements may not be as significant as usually suggested. In both readings, the implied subject of the clause is the manager.

I saw Pam going home.

This is the ambiguous sentence, where two interpretations of who is going home are possible. That is, the non-finite clause can be read as either supplementive or complementive. That means that the intonation doesn't give away the semantics of the sentence.

 

[diamondcutter]

Does the author mean this?
For sentence [2], it doesn’t produce difference in meaning whether you look upon the participle “smiling” as complementation of the verb “approached” or as a supplementive clause.

 

[jutfrank]

In [2], the clause is a complement. In [1], it's a supplement. They're supposed to be contrasted. He's saying these are two ways of intoning the same sentence, the difference being only the focuses of information. We can tell whether the clause is complement or supplement by the way the speaker intones.

 

[diamondcutter]

"That means that the intonation doesn't give away the semantics of the sentence."

Hi, Jutfrank.
Did you mean to say "does give away" instead of "doesn't give away"?

 

[diamondcutter]

I’ll try to paraphrase what the first two paragraphs want to say in Page 1126 of the book.

When a present participle occurs in the final position of a sentence, it’s not always necessary to put a comma before it. Taking the following two sentences as an example, they have the same meaning and just a little difference, which is that [1] has two focuses of information, whereas [2] has only one:
The manager apPROCHED us, SMILING. [1]
The manager approached us SMILING. [2]

However, sentences are different from sentences. In some sentences, if a comma is not used, they will be ambiguous, for example, the following one:
I saw Pam going home. [3]

What do you think of my paraphrasing?

 

[diamondcutter]

Dear teachers, please excuse my silliness, but I really need your help. Would you please spare a little time to answer my questions? I would appreciate it greatly if you could.

 

[jutfrank]

Did you mean to say "does give away" instead of "doesn't give away"?

No.

What do you think of my paraphrasing?

Let's have a look:

When a present participle occurs in the final position of a sentence, it’s not always necessary to put a comma before it.

It isn't saying anything at all about comma usage. The comma is just the way of representing the intonation in writing.

Taking the following two sentences as an example, they have the same meaning and just a little difference, which is that [1] has two focuses of information, whereas [2] has only one:
The manager apPROCHED us, SMILING. [1]
The manager approached us SMILING. [2]

Right.

However, sentences are different from sentences. In some sentences, if a comma is not used, they will be ambiguous, for example, the following one:
I saw Pam going home. [3]

No, that's not right.

I saw Pam going home.

On one interpretation, you can analyse going home as a supplementive clause (with I as the implied subject), even though there's no intonation (or comma) separating it from the main clause. It illustrates the point, which is that "supplementive clauses need not be separated from their matrix clause intonationally when they occur in final position."