There are several reasons a chamber can burst or fail.
Yes. Hyperbaric chambers Exploding. Yes they can actually. (deflate rapidly is a better term a there is no explosion, just a rapid decrease in pressure that can be super loud when you are in it.
1. Over pressurization. Some people think more is better. They will do stupid thinks like plug up or manually disable the pressure relief valves. These valves are critical to the safety of the chamber. These little valves are calibrated to open at 4 PSI. Once they open they should stay open to circulate the CO2 out and allow fresh air to come in the chamber. Defeating the valves can cause a build up of CO2 and can cause the failure of the chamber.
Some chambers have tamper proof pressure relief valves. These chambers are safer than manufacturers who have adjustable valves. You can tell if it has an adjustable valve, as there's a little screw for adjusting on the inner side of the valve.
2. Improper closing of the mechanical zippers can also cause chambers to burst. Usually if the airtight zipper is not sealed all these way the hyperbric chamber won't fully pressurize. The zipper has to be completely closed. Some have a security strap that the zipper goes through so the zipper can't be accidentally opened when the chamber is even pressurized just a little bit. Also if the zipper (the mechanical zipper, not the air tight one) is not 100% closed it can cause the chamber to burst.
3. Another cause of bursting is a window seam opens up under pressure. Some manufacturers have a weld to secure the window to the chamber that is ½ inch wide. Their are even some chamber windows that have a steel bulkhead. There are hyperbaric chambers that now have multi layered windows, up to 5 ply with multiple wide welds. So if one weld fails the chamber should still stay pressurized and not burst. 5 ply is the highest I have seen. This is especially important if the chamber ever goes over 1.3 ATA. Many companies have 3 ply and if no one is tampering with their chamber or going above 1.3 ATA, there usually should not be any problems.
4. The last cause of a chamber bursting or rapidly losing pressure is welded bulkheads that hold the valves and gauges. The bulkheads that are mechanical are the strongest that I have seen. They literally screw together compressing the vinyl. I also look to see if the chamber has a reinforcing layer of material where the bulkhead is located.
So those are the most common reason that come to mind when considering a hyperbaric chamber exploding or bursting. I give this the most importance on chambers that have valves making them go to over 1.3 ATA. The ones that have 3 zippers are usually much more expensive than the 2 zipper chambers. Usually the bigger chambers.
Note: just so people know, I am the one that hears the stories first hand from people that have the failures in their chambers. People always complained that the zippers failed on the Newtowne and they think I'm the guy to return it to. (Note the new Seal just came out and I have not heard of any zipper problems anymore). Usually it a window seal leaking is the most common problem. Hopefully, people will be more informed and companies can't get away with trying to cut costs on components of the chamber as people know the rights questions to ask.