I'm not an electonicker, but here's my understanding of how a GFCI works. Think of wiring two transformers in series with the load - one on the "hot" side and one on the "neutral" side. Then connect the secondaries of the transformers in series, with one of them reversed. As long as the amount of current coming in on the "hot" side is exactly the same as the amount of current leaving on the "neutral" side, the two secondary voltages will be exactly the same. So they'll cancel each other out and the series voltage will be zero. Now introduce a little bit of leakage to ground somewhere in the load. When this happens, the outgoing current will be different from the incoming ... part of it is taking a different path. So the voltages of the two secondaries will differ and they won't cancel exactly. A circuit in the GFCI detects this small voltage, and if present, it will trip the switch.
I read somewhere that a GFCI will trip if the imbalance between gazinta current and gazata current is as low as 5 milliamps. That's below the threshold of harmful current for a human being. So a GFCI is designed to save your life.
Two failure modes are possible - either the GFCI will fail to trip at 5 milliamps or higher, or else it might trip at a much lower threshold. I'm pretty confident that the GFCI circuitry is well designed to be fail-safe, so the former scenario won't happen. But the latter scenario remains possible and would result in nuisance tripping.