If this actually happened, you need to go to a medical facility right away and document the injury - get imaging, medical reports, everything in chronological order. Then take it to the prosecutor's office or go straight through a lawyer. A punctured lung is a serious injury that needs to be investigated and compensated. The salon is liable, even if it was some extremely rare procedure.
As for how something like this could even happen - it could be a procedure like injections, microneedling, or something along those lines done on the back or chest area. The technician just didn't know anatomy or worked carelessly without understanding where vital organs are located. Sure, there are licensing and training requirements on paper, but in reality salons hire people who took short courses, and oversight is weak.
You'd think qualification checks would be needed, but here's how the system actually works: a salon needs a license, technicians need certificates. On paper it all looks fine, but in practice a lot of establishments hire people without proper training or they use questionable techniques. If this happened to you or someone you know, don't stay quiet - that's the only way anything changes.