That can be passed without ever even doing a Liver Flush or even ingesting copious amounts of oil.
Or "fecal soaps" that reside in the intestines for extended periods of time.
If you are not getting any fats in your diet then you would be extremely unhealthy if not dead. So you have a source in your diet that would allow for saponification. All you have to do now is to look up digestive transit time to put the rest of the puzzle together.
By the way, why are you picking through your feces if you are not even doing a flush or supposedly consuming any oil? This seems to be a theme with the "liver flush" supporters! Personally I have real hobbies and can think of a lot of other things I would prefer to spend my time on.