How to limit a bone between other two bones, for scale and position I have this situation: 



I want the bone "A" to always be between the other two bones, extension included. This bone receives user movement, grab and scale, using any number of extra bones. 

I already tried to give bone "A" constraints like Floor and that worked nice, but it doesn't work for the other handle of the bone. 



This second image show an auto adjustment making this effect, using Floor and  Stretch, but the interaction bone (the selected one) lacks for limits in it's extreme, making it imprecise.
I'm not entirely sure what you're asking, but I'll take a guess:

If you want A's base to be at B's base and A's tip to be at C's base, you might benefit from drivers.  

Unfortunately, the expressions to map from B and C to the proper pose for A would not be trivial.

Also, blender has some shortcomings in its dependency system that prevents intra-armature drivers from being calculated correctly in some circumstances.