Why doesn’t a house fill with gas when the pilot light goes out? I WAG the flame may draw gas off a header via a venturi, perhaps, to cause negative pressure to feed the flame? Otherwise, gas cannot flow into this mini supply line (i.e: the venturi)?
The pilot light uses a really small amount of gas.
Most things with pilot lights have a thermostatic switch associated with the pilot light that has to be kept hot other wise it shuts down the gas to the pilot light. I know both my house heater and hot water heater have this with the pilot light.
Gazpacho -
Thanks for the info, and might you have a gazpacho recipe?
Seriously! 
-Jinx
The common name for the safety device is a Thermocouple. It is also a wearing part and has to get replaced on average every 10 years or so (both your gas furnace and gas water heater will have one). Generally, if your pilot light won’t stay lit, its because that little gizmo is worn out.
most are but I just replaced one that was simply a piece of metal that ran through a rather large pilot light (triple flame) the expansion of the metal kept the gas flowing.
Also some oven’s and stoves don’t have an auto shutoff valve.