Because Hyperbaric chambers are designed to support a certain amount of atmospheric pressure, it is not possible for chambers to exceed designed capacity - even if they wanted to. Most soft-shell models support up to 1.3 ATA, with clinic-grade chambers capable of supporting up to 6 ATA.
In addition, Hyperbaric chambers are designed and rigorously tested to ensure that combustion due to over-pressurization is prevented at all costs. HBO chambers are continually being assessed and improved, most frequently in the device’s initial stage of assembly.
To date, there is no recorded history of any user experiencing chamber combustion due to over-pressurization.