In vision, Augmented Reality (AR) allows the superposition of digital content on real-world visual information, relying on the well-established See-through paradigm. In the haptic domain, a putative Feel-through wearable device should allow to modify the tactile sensation without masking the actual cutaneous perception of the physical objects. To the best of our knowledge, a similar technology is still far to be effectively implemented. In this work, we present an approach that allows, for the first time, to modulate the perceived softness of real objects using a Feel-through wearable that uses a thin fabric as interaction surface. During the interaction with real objects, the device can modulate the growth of the contact area over the fingerpad without affecting the force experienced by the user, thus modulating the perceived softness. To this aim, the lifting mechanism of our system warps the fabric around the fingerpad in a way proportional to the force exerted on the specimen under exploration. At the same time, the stretching state of the fabric is controlled to keep a loose contact with the fingerpad. We demonstrated that different softness perceptions for the same specimens can be elicited, by suitably controlling the lifting mechanism of the system.