What happens if the helium pressure gets too high? Do you just pop?
Nope. There is an inflatable/deflatable air cell inside the envelope called the ballonet. It can be inflated or deflated as required in flight to maintain pressure within limits. We have two air ducts at the rear of the gondola, one behind each engine, that capture slipstream air from the propellers, and divert them through check valves into a plenum chamber, and from there into the ballonet. Thus the ballonet compensates for changes in helium volume to maintain a given pressure range.
There is a condition called "pressure height" which occurrs when the ballonet reaches zero volume. In fact, pressure height is what limits how high we can climb on a given day. When the ballonet reaches zero volume, any further decrease in atmospheric pressure (altitude), increase in atmospheric temperature, or any combination thereof, will cause the pressure to continue to increase (because we can't force any more air out of the ballonet, there's nothing left inside it). If you want to climb above pressure height, the only way to do so is to get rid of helium. We generally try to avoid valving helium unless absolutely necessary, becuase doing so causes us to lose static lift, and helium is expensive to replace.
Realisically, there aren't very many situations that would cause envelope failure. Getting caught in the updrafts associated with convective activity is one situation that could do it, however.
Oh, and sorry for the verbose explanation. There isn't really a simple way of describing how we operate though to those unfamiliar.