Deer have a evolutionary adaptaion that enables them to shut down venus circulation to wounds thereby preventing blood loss. I can envison an arrow passthrough between lungs and spine, which didn't hit an artery, and was then plugged with fat and other tissue to prevent a sucking chest wound, as not being lethal given their ability to control bleeding.
Ironically it's my favorite rifle target on an undisturbed deer. Such a hit from a fast bullet deflates the lungs and disrupts the nervous system causing near instant death by shock with a minimum loss of edible meat.