When droplets impact fibrous media, the liquid can be captured by the fibers or contact then break away. Previous studies have shown that the efficiency of drop capture by a rigid fiber depends on the impact velocity and a threshold velocity was defined below which the drop is captured. However, it is necessary to consider the coupling of elastic and capillary effects to achieve an improved understanding of the capture process for soft substrates. Here, we study experimentally the dynamics of a single drop impacting on a thin flexible fiber. Our results demonstrate that the threshold capture velocity depends on the flexibility of fibers in a non-monotonic way. We conclude that tuning the mechanical properties of fibers can optimize the efficiency of droplet capture.