The structural modifications and orientational ordering of nematic (5CB) droplets with the bipolar director-field configuration, embedded in a uniaxially stretched polyvinyl alcohol (PVA) matrix, are studied using polarized optical microscopy. It has been found that the unidirectional ordering of droplets with stretching takes place in two stages. At small matrix deformations, each bipolar structure is captured by the surface of the droplet cavity, so that the bipolar axis makes an angle with the long axis of the cavity and therewith is gradually rotated toward the stretch direction in accordance with the affine transformation of matrix dimensions. As the droplet non-sphericity further increases, there comes a point where the elastic deformation energy of the captured structure overcomes the surface interactions and, as a result, the droplet abruptly reorients parallel to the long cavity axis. The measurements of the orientational distribution function have testified the pronounced threshold nature of the bipolar droplet’s ordering process. It has also been found that the heating of the slightly elongated polymer matrix above its glass transition temperature eliminates the captured structures and produces the irreversible uniaxial orientation of the sample. From these findings, it is inferred that the formation of the supramolecular polymer structure at the matrix/droplet interface during the matrix curing process and its changes with stretching and heating are the governing factors responsible for the bipolar droplets. A model is proposed which substantiates this conclusion in terms of the polycrystallline morphology of the PVA matrix. Finally, the applicability of the results is briefly discussed from both fundamental and applied points of view.