I spent 30 years in the oil industry. I started in 1986 with Chevron when the price of oil was at one of its lowest points in decades. I was offered the job just before the price collapsed. Chevron honored that offer and never let me go despite numerous layoffs over the next ten years. It was true that Chevron considers new hires "safe" so they can learn what it is they have just acquired. However, I am not sure I would count on this in your case because you were actually hired by Anadarko.
There is also long-standing bias in the oil field not to trust someone else's hiring practices so not sure where you will fall will this one. The oil industry is a bumpy ride to say the very least so even if you survive this one you can be sure there will be others coming and likely they will be coming one after the other. Keep your resume and network updated constantly. Good luck.