Good question, followed by good points. You have some examples in scripture of this: Luke 15
Are these examples applicable to believer that falls away? Possibly, I think that could apply. But Jesus is speaking of those that are already in the fold, and bringing them back into the fold.
So why would Jesus only concern Himself with only the saved > lost? Because we are ALL not saved at some point.
What I understand from what you are saying is Jesus came to save then look for those that are lost? that doesn't make much sense when we are all born into sin, lost, without the Holy Spirit.
Those that do not believe, are surely lost.
I could be misunderstanding what you are trying to say. I am tired