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In my past thread, I asked a question about the "interpretation of using."
From the comment and advice I received, I still believe that the following interpretation is true:

1. They will show the examples using this method. (=which use)
2. They will show the examples, using this method. (=and they will use)

However, I wonder if there is a possibility that even native speakers sometimes omit a comma but still mean the case #2 above. For instance, in the following example, is there a possibility that even a native speaker interprets the sentence as "Execute the database with the use of the generator" instead of "Execute the database which uses the generator"?

Example) Execute the database using the generator.
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You're probably right that native speakers are often careless about punctuation. If you want to avoid ambiguity you can re-write the two sentences as follows:

1. They will show the examples that use this method.
2. They will show the examples by using this method OR They will use this method to show the examples.

However, it's usually clear from the context what meaning is intended.
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GoriI found an article of "no comma + ~ing" form as shown below. In this example, does "asking" modify "a fax" or does this sentence simply miss a comma before "asking"?

"Around 11 p.m., ward education board officials sent out a fax to 31 principals of elementary and junior high schools in the ward asking them to investigate possible bullying."
Well, you can say that:
the fax was asking them to ...
but in effect it was
the board officials who were asking them to ...
(a fax has no intelligenceEmotion: smile)

To me this sentence is clear.
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Comments  
I found an article of "no comma + ~ing" form as shown below. In this example, does "asking" modify "a fax" or does this sentence simply miss a comma before "asking"?

"Around 11 p.m., ward education board officials sent out a fax to 31 principals of elementary and junior high schools in the ward asking them to investigate possible bullying."
 Marius Hancu's reply was promoted to an answer.
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