When I learned this, it had a very distinctive name and allowed to make more interesting sentences. For instance, given the sentence
Fred extended his feet, which stopped the car.
It can be rephrased as
Fred extended his feet, stopping the car.
How is this construct called and is the comma still necessary?
"Stopping the car" is a present participle phrase, and it does change the meaning of the sentence in a minor way. In the first sentence, the extension of Fred's feet is what stopped the car. (Or, I suppose you could also view it where "which" refers to "his feet," and his feet stopped the car.) In the second sentence, Fred is what stopped the car (though he clearly did this by extending his feet).
The comma is necessary to convey the same meaning in the second sentence. Otherwise, Fred simply extends his "feet stopping the car," which doesn't make much sense.
In your second example, the comma helps clarify who or what is being modified by the participle phrase. In "Fred extended his feet, stopping the car", the comma separates unlike terms. It tells us that stopping the car does not modify feet. Instead, it modifies another word earlier in the sentence. Fred. To remove the comma is to link feet and stopping the car, to say that stopping the car does modify feet. And Fred extended his feet stopping the car sounds odd because feet don't normally stop cars, brakes do. That is, unless we are talking about Fred Flintstone. In which case, it might be better to say something like:
Fred extended his feet gouging the dirt and stopping the car.
So, in answer to the question about comma placement with participle phrases, you would be correct with or without the comma, but only because you're talking about the Flintstones.
