Soft grippers’ rising popularity in industries is due to their impressive adaptability. Yet, this adaptability requires flexibility which often sacrifices grip firmness and complicates sensor integration. This paper introduces two additional innovations, variable stiffness and pneumatic sensing, into a FinRay adaptive gripper. The approach and design for incorporating these innovations are guided by requirements outlined by FESTO. Regarding this, a layer jamming-based variable stiffness skin broadens gripper applications, manipulating objects of varying hardness and weight, while a pneumatic sensor skin detects contact and loss of contact. Both functionalities rely on the airtightness of the skins, which is compromised if damaged. To address this, both the skins and the gripper were crafted using self-healing polymers. The sensing and modulated mechanical performance of the gripper were evaluated experimentally and through simulations, and the selfhealing ability was assessed by recharacterization after a damage-healing. This work showcases the promising synergy between robotics and self-healing materials, demonstrating mutual reinforcement to a highly efficient gripping system.