Despite the importance of softness, there is no evidence of wearable haptic systems able to deliver controllable softness cues. Here, we present the Wearable Fabric Yielding Display (W-FYD), a fabric-based display for multi-cue delivery that can be worn on user's finger and enables, for the first time, both active and passive softness exploration. It can also induce a sliding effect under the finger-pad. A given stiffness profile can be obtained by modulating the stretching state of the fabric through two motors. Furthermore, a lifting mechanism allows to put the fabric in contact with the user's finger-pad, to enable passive softness rendering. In this paper, we describe the architecture of W-FYD, and a thorough characterization of its stiffness workspace, frequency response and softness rendering capabilities. We also computed device Just Noticeable Difference in both active and passive exploratory conditions, for linear and non-linear stiffness rendering as well as for sliding direction perception. The effect of device weight was also considered. Furthermore, performance of participants and their subjective quantitative evaluation in detecting sliding direction and softness discrimination tasks are reported. Finally, applications of W-FYD in tactile augmented reality for open palpation are discussed, opening interesting perspectives in many fields of human-machine interaction.