could the rear differential cause a a tire to completely FALL OFF while driving?

What is your question?

We were driving down highway and started to feel the back end of the truck start to shake. Then it started to feel like we had a flat tire. We were less than a 1/4 mile away from the gas station when the tire JUST SHOT OFF THE TRUCK!(went flying deep into the woods). We then slid across the road about the length of a football field. Luckily we did not flip and there were no other cars around us at the time. could this be caused by the rear differential or is there a bigger issue we over looked? Please help someone!!