Where does all the scale inside your pipes go after you fit a water softener?
The scale is softened to a point where it becomes a minimal concentration of hardness, which comes out your tap.
The hard water comes into the house with a hardness of approximately 300 ppm, which is reduced to almost zero by the water softener.
Water that has almost no hardness will want to dissolve rather than precipitate hardness. As this softened water goes into the pipe, it starts to gradually dissolve the chalk and lime in the pipe. It will come out of your tap with a hardness of 10-15 ppm.
This minimal concentration of hardness then passes through the system as the water is used.
You cannot taste this concentration and it poses no health risks.