Control of particle shape is of increased interest, as it can broaden the versatility of dispersed material applications. The design of targeted and selective response, such as shape-change, in synthetic materials offers an opportunity to mimic and understand biophysical motion, but also enhance commercial active material delivery. Although solids can experience a wide range of shape-change behavior, soft materials like viscoelastic droplets are also quite versatile, exhibiting shape-change and localized wrapping when triggered by external temperature or stress fields. Here we show, with elastocapillary concepts, that viscoelastic droplets can self-trigger shape-change and wrapping behavior in response to physical contact with targets below a threshold curvature. The model is in good agreement with experimental data on interactions between rod-shaped endoskeletal droplets and cylindrical targets of varying curvature. The concept of a pre-programmed physical sensing and response by simple, soft material shapes is explored and used to suggest additional applications and more complex applied modeling, shape designs, and responses.