When the engine is first started, and rpm is above 400 rpm, the system goes into 'Open Loop' operation. In 'Open Loop', the PCM will ignore the signal from the Oxygen (O2) sensor and calculate the air/fuel ratio based on inputs from the coolant and MAF sensors, but mostly from a pre-programmed table in the memcal. The system will stay in 'Open Loop' until the following conditions are met:
- The O2 sensor has varying voltage output, showing that it is hot enough to operate properly. (This depends on temperature)
- The coolant sensor is above a specified temperature about 40oC/104oF.
- A specific amount of time has elapsed after starting the engine.
The specific values for the above conditions vary with different engines and are stored in the mem-cal. When these conditions are met, the system goes into 'Closed Loop' operation. 'Closed Loop" is the normal operation mode of the PCM. In 'Closed Loop', the PCM will calculate the air/fuel ratio (injector on-time) based on the various sensors but mainly the O2 sensor.
Running the system in 'Open Loop' will ignore the O2 sensors and you can use that to "bandaide" out a lean running condition. But your fuel economy will suffer from it.
As for why a tune would stay in 'Open Loop'? First thought would be that the tuner wrote it that way. If not, then I would suspect a PCM issue.