We report results of large-scale molecular-dynamics (MD) simulations of dynamic deformation under biaxial tensile strain of pre-strained single-crystalline nanometerscale- thick face-centered cubic (fcc) copper films. Our results show that stacking faults, which are abundantly present in fcc metals, may play a significant role in the dissociation, cross-slip, and eventual annihilation of dislocations in small-volume structures of fcc metals. The underlying mechanisms are mediated by interactions within and between extended dislocations that lead to annihilation of Shockley partial dislocations or formation of perfect dislocations. Our findings demonstrate dislocation starvation in small-volume structures with ultra-thin film geometry, governed by a mechanism other than dislocation escape to free surfaces, and underline the significant role of geometry in determining the mechanical response of metallic small-volume structures.