Moulting
Pictured is a Metallic female (Achrioptera Fallax) moulting to adulthood.
Prior to moulting they will stop feeding and anchor their feet to a branch, leaf or mesh.
They will expand their bodies to enable them to break through their old skin and pull free.
Their bodies are much softer under their old skin. Once free they will hang for some time to dry and harden their new skin.
At the base of each limb are white strands, like safety lines, attached to the old skin to support their weight until the limbs have dried and are strong enough to support themselves.
Many stick insects will eat their old skin soon after moulting. This is recycling the nutrients that may be left in the old skin.
Moulting can be the biggest danger to any invertebrate, including stick insects, which are often kept communally so are at increased risk of being disturbed or dislodged.
Mismoulting
If they lose their grip and fall in the process of moulting HANG THEM BACK UP IMMEDIATELY!