Here is a interesting article from phys.org about modifying superconductivity using stress. Film stress in the semiconductor industry can change electrical properties of conductors so this makes perfect sense.
At an atomic level the concept of stress is simply the distance between atoms or molecules. In an equilibrium state the atoms want to be a specific distance from each other. Due to the formation process the atoms may be a little too close or too far from each other. Technically this is not an equilibrium state, but the positions can be locked in place so that it is difficult for the film to relax. Moderate levels of compressive and tensile stress can be stable in the long term.
It would be interesting to deposit some high temperature superconductors at a variety of film stresses ranging from compressive to neutral to tensile and see how the critical temperature and critical magnetic field depend on the stress.