Shape displays are a class of haptic devices that enable whole-hand haptic exploration of 3D surfaces. However, their scalability is limited by the mechanical complexity and high cost of traditional actuator arrays. We propose using electroadhesive auxetic skins as a strain-limiting layer to create programmable shape change in a continuous (“formable crust”) shape display. Auxetic skins are manufactured as flexible printed circuit boards with dielectric-laminated electrodes on each auxetic unit cell (AUC), using monolithic fabrication to lower cost and assembly time. By layering multiple sheets and applying a voltage between electrodes on subsequent layers, electroadhesion locks individual AUCs, achieving a maximum in-plane stiffness variation of 7.6x with a power consumption of 50 µW/AUC. We first characterize an individual AUC and compare results to a kinematic model. We then validate the ability of a 5x5 AUC array to actively modify its own axial and transverse stiffness. Finally, we demonstrate this array in a continuous shape display as a strain-limiting skin to programmatically modulate the shape output of an inflatable LDPE pouch. Integrating electroadhesion with auxetics enables new capabilities for scalable, low-profile, and low-power control of flexible robotic systems.