Understanding how a turbofan engine works, they function on the principle that a turbojet engine is gear-coupled with a much larger outer fan that in turn provides much of the thrust via bypassing bulk incoming air. That bit established...
My idea is experimental in the idea that on most planetary bodies we encounter, there's a lack of oxygen to burn with normal engines but they do have atmospheres that the fans can take advantage of. As far as the engine is concerned, it only requires a supply of oxygen to burn properly. Of course, normal air is only about 30 percent oxygen and the remainder is a mix of inert gases that absorb the extra heat, thus assisting the turbines due to thermal expansion while minimizing overheating of the engine's interior.
The same can be said if you only allowed 70% inert gasses into the turbine then added 30% oxidizer and appropriate fuel to the mix and ignited. This would still provide thrust, and would turn the turbines, adding significantly more thrust depending on atmospheric densities at the fan inlet. Granted, it wont get you into orbit due to it's obvious subsonic design considerations, but may be the fuel efficient kick needed to swim through (and out of) the thickest of atmospheric layers.
In conclusion, this would be the equivalence of a small subsonic rocket motor with turbined expansion bell feeding a larger outer fan for added efficiency. Higher atmospheric ISP/thrust, very low vacuum ISP/thrust, moderate drag due to large fan area, thus subsonic by design.