Adversarial attacks on point clouds often impose strict geometric constraints to preserve plausibility; however, such constraints inherently limit transferability and undefendability. While deformation offers an alternative, existing unstructured approaches may introduce unnatural distortions, making adversarial point clouds conspicuous and undermining their plausibility. In this paper, we propose CageAttack, a cage-based deformation framework that produces natural adversarial point clouds. It first constructs a cage around the target object, providing a structured basis for smooth, natural-looking deformation. Perturbations are then applied to the cage vertices, which seamlessly propagate to the point cloud, ensuring that the resulting deformations remain intrinsic to the object and preserve plausibility. Extensive experiments on seven 3D deep neural network classifiers across three datasets show that CageAttack achieves a superior balance among transferability, undefendability, and plausibility, outperforming state-of-the-art methods. Codes will be made public upon acceptance.