I had this happen once on a John Crane 2800 double dry gas seal. This one was a very unusual case in an old seal design. I don't think it would be possible in a properly designed new system to fail in this manner. I will describe the failure that we experienced.
This seal was in a single stage overhung Roots machine running about 12,000 rpm. The seal was supplied with nitrogen gas using a very crude system. They had a regulator and a local flow meter with no instrumentation to alarm on loss of nitrogen flow.
The nitrogen connected to the seal using 1/2" SS tubing. A few inches away, on the side of the case, there was another piece of 1/2" tubing that was in impulse line to a panel mounted instrument that read process pressure. After an overhaul of the compressor, the mechanic reversed the two pieces of tubing. The area between the two seals was connected to the pressure gauge on the panel and the nitrogen was dumping into the case connection. After some time in service, they started leaking process gas out along the shaft. Both seals had failed catastrophically because there was no nitrogen flowing to the seal. The stationary seal face shattered and pieces of tungsten carbide dropped down onto the shaft and machined through the seal sleeve and about 1/4" deep into the shaft before we got the machine shut down.
At any other similar installation, we would have instruments to control the nitrogen buffer gas to a certain differential pressure above process pressure. We would monitor the buffer gas flow rate, as well. As long as nitrogen DP was maintained it should be impossible for process gas to leak directly to atmosphere past both seals. I don't believe we would trip the compressor off on loss of buffer gas DP. But we would definitely alarm and take immediate action to restore buffer gas flow or shut the unit down.
So, from a HazOp standpoint, I don't believe a double dry gas seal properly instrumented for differential pressure and buffer gas flow rate should ever fail catastrophically enough to blow process gas directly to atmosphere past both seals. From a HazAn, LOPA standpoint, this should be in the category of 1/100 years or less.
Johnny Pellin