Pilot light continually burning
Gas fired appliances usually have a standing pilot that is monitored or one of several types of igniters, spark igniters usually you can hear the click, click click, hot surface igniter several types here coils if nichrome wires that get red hot and a carbon like material that gets hot and ignites the gas all 3 that ignite the main burner do not have a pilot. The type that has a standing pilot the pilot is always lit. 

Standing pilots are going out of style because of the constant use of gas. The bummer about this is standing pilots are much more reliable than any of the other methods. 

If you notice the gas going off I believe you are remembering the temp being made and the main burner shutting down. As if the pilot shuts down this will normally cause the thermocouple to cool and will normally shut the gas down unless there is a system to monitor the flame. With the information provided I believe you are not accurate in your memory of events but a model number would help verify the normal operation.