Can Unity lighting create baked shadows? Not realtime

Imagine 1 cube, and then there is point light. I want to bake soft shadow from cube, which will be baked directly into texture instance of floor, where cube stands. This shadow will be basically like someone drew dark shadow on texture and that's all. Not affecting realtime objects. I mean if I will remove cube in editor and NOT rebuild lighting - shadow should be still present.

 

If I understand your question, this is exactly how manual lightmap building works. You need to turn off the automatic, set everything up, bake, save, and then it will stay this way, as far as I know even into the build process.

Keep in mind to bake lighting, everything involved (lights and geometry) must be marked Lightmap Static or else it is ignored. This is by design.