The four stretchiness buttons determine whether the limbs can stretch or not. In the picture above the left side is stretchy, but the right side is not. There is a difference between FK and IK here. An FK limb can stretch even if the elbow or knee is bent, but an IK limb that stretches is always straightened out first.

The buttons that change stretchiness go into edit mode to change connectivity. They can hence not be invoked with file linking. To toggle stretchiness on or off can only be done in the master file.