We present a novel shape-shifting haptic device, Shiftly, which renders plausible haptic feedback when touching virtual objects in Virtual Reality (VR). By changing its shape, different geometries of virtual objects can be approximated to provide haptic feedback for the user's hand. The device employs only three actuators and three curved origamis that can be programmatically folded and unfolded to create a variety of touch surfaces ranging from flat to curved. In this paper, we present the design of Shiftly, including its kinematic model and integration into VR setups for haptics. We also assessed Shiftly using two user studies. The first study evaluated how well Shiftly can approximate different shapes without visual representation. The second study investigated the realism of the haptic feedback with Shiftly for a user when touching a rendered virtual object. The results showed that our device can provide realistic haptic feedback for flat surfaces, convex shapes of different curvatures, and edge-shaped geometries. Shiftly can less realistically render concave surfaces and objects with small details.