Essential vs. non essential modifier question

[yo4561]

Happy Wednesday!

I realize that MP says generally the rule of thumb is as follows (but not always):
no commas = essential
commas= nonessential

Then, MP shows the following example:
"The engineer fixed the problem, earning herself a promotion."

Is this an example where essential information happens to be offset by a comma? To me "earning herself a promotion" seems pretty important. If not, can you please provide an example where this rule of thumb for commas vs. no commas to determine essential vs. non essential would come to play?

Have a joyous day my friends

[esledge]

Hi yo! I think this rule...

no commas = essential
commas= nonessential

...should mainly be applied when comparing noun modifiers to noun modifiers. These are all noun modifiers:

Essential: The dog that licked my ice cream is a beagle.
Nonessential: The dog, which is a beagle, knows how to sit, shake hands, and roll over on command.
Essential: The doctor who presented at the conference this morning is an expert in her field.
Nonessential: The doctor, who has worked at County General for 15 years, will be on maternity leave for 6 weeks this fall.

When you have a mixed bag of adverbial modifiers and noun modifiers, the comma instead might indicate noun/adverbial modifier status:

Noun modifier: The cat hunching down in the grass is preparing to pounce. (Which cat is preparing to pounce?)
Adverbial modifier: The cat hunched down in the grass, preparing to pounce. (Why was the cat hunched in the grass?)