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.