To clarify regards MAF: (this sensor measures the quantity of air entering the intake)
If it 'fails' ie stops providing a reading or one thats detected as faulty as its out of limits, then you WILL get a light on the dash (ESP/traction control light).
The car will then run using alternative data but not in limp mode.. it will actually run near to normal power, some people wouldnt even notice. Its likely to run a little rich.
However the other
problem people may report with the maf is reading low, in this case its providing a reading which is within limits so the ecu does not detect an error, but the figure provided is lower than it should be so the engine runs down on power.
As said above, this is not limp mode, but rather a sensor reading incorrectly (less air, less power) and as a result the engine produces less power than it should as it uses the incorrect data from the sensor.
Limp mode is where the ecu has detected an error and limits boost to prevent further damage. Limp mode depending on the fault may or may not reset after ignition off/on.