Has anyone survived falling from a plane with a faulty parachute?

Yes for sure. I read a book once about a WW2 B-17 bomber crewman who fell from 5,000 feet, with a faulty parachute, and landed at an angle on a mountain with powdery snow that allowed him to sustain only minor injuries. The book is called Bomber Boys if you want to check it out. I highly reccomend it.