You cannot stretch this system along A. The ribbon lies in the BC plane, so it can only be strained there.
The best way to strain such a system is while it's still periodic, i.e. before the turn it into a ribbon. Then you can easily decide to use uniaxial or hydrostatic strain (area expansion) when you set up the basic unit of the 2D material. Then you repeat and terminate the strained structure. If you relax the lattice constants of the strained crystal it will go back to the unstrained case, but you can relax the forces (positions) to capture surface reconstruction.