Self-wrapping, braided textile sleeve with self-sustaining expanded and contracted states and method of construction thereof

A method of constructing a self-wrapping textile sleeve, comprising:

• braiding a plurality of yarns with one another to form a wall extending lengthwise along a central longitudinal axis between opposite ends with at least some of said yarns being provided as heat-settable yarns, said wall being moveable between a decreased length, increased cross-sectional area first state and an increased length, decreased cross-sectional area second state;
• forming said wall having opposite free edges extending lengthwise between said opposite ends;
• and
• wrapping said opposite free edges toward one another and heat-setting said heat-settable yarns with said wall being in one of said first state and second state to form heat-set yarns that impart a bias on said wall, said bias causing said wall to self-wrap about the central longitudinal axis into a tubular configuration and causing said wall to remain in each of said first and second states absent an externally applied axial force causing said wall to be moved to the other of said first or second states.