Micron-scale rod-shaped droplets with a range of aspect ratios are produced using extrusion of oil containing a soft wax crystal network to permit shape customization. A physical model of the droplet shape stability is developed based on balancing interfacial stresses with the internal crystal network yield stress. The model predicts the mechanical properties required for particular droplet size stability, in a given physicochemical environment, and is tested by microscopic observations of droplets over a range of relevant applied temperatures. The time-dependent response to temperature of individual rods is monitored and used to identify the collapse temperature based on structural yielding. Precise temperature control allows variation of the droplet endoskeleton yield stress and direct determination of the droplet stability as a function of size, by observing the onset of collapse by interfacial compression, and enables validation of the model predictions. Mapping the regions of droplet stability and instability for various-sized droplets yields a basis for designing droplet shapes for multiple applications using easily measured physical variables. The phenomenon of arrested collapse is also explored as a means of transforming simple rod-shaped starting materials into more complex shapes and enhancing adhesion to targeted solid surfaces, enabling exploitation of the hybrid solid-liquid nature of these droplets.