The lungs work to suck air in by creating a difference in pressure due to vacuum. If you perforate one of your lungs, a vacuum is no longer present and the lungs cannot work. This is obvious. Without Oxygen, you die in minutes. So you are right that you won't die instantly, but for all practical effects it is the same.
SUCKMYMUSCLE
Sweetheart,
If left for a prolonged period of time, yes you can die from what is known as a tension pneumothorax (very rarely does this ever occur). For the most part and in most situations, what you will develop is a pneumothorax (an accumulation of air between your lung and chest wall) on the side of the affected lung. While dealing with a pneumothorax is no fun for anyone, you can certainly breathe while it's present. What they do for such things depends mainly on the actual size of the pneumothorax, some cases are just kept in observation and resolve, while other cases require the insertion/placement a chest tube onto the affected side, which in turn restores the negative pressure needed for your lung to re-expand.
So, again, it is much more probable that a gym goer will suffer from a complete lesion to the C1-C7 cervical region of the spine, by way of a heavy squatting injury, that causes instant quadriplegia.
I love you sucky,
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1"