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.
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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."