I will describe recent experiments that characterize an interesting dynamical transition deep in the shear-jammed phase of frictional granular materials. Shear-induced jamming is relevant in a large variety of disordered, complex systems. For example, discontinuous shear-thickening in some non-Newtonian fluids is found to depend on the proximity to a frictional shear-jamming transition. The stability of shear-jammed states, however, remains poorly understood. To shed some light on the problem, we perform experiments that monitor the evolution of shear-jammed states under controlled perturbations in the form of small amplitude periodic shear. These experiments involve photoelastic techniques that measure all inter-particle contact forces, and recently developed apparatuses that sample sheared states below the random close packing in a way mimicing the AQS algorithm. Our experiments show that most shear-jammed states, even with a highly percolated force network, are surprisingly unstable and collapse completely under even weak perturbations.However, in some cases, the system evolves into a different jammed state in which all the microscopic degrees of freedom, including all contact forces, become reversible in the long time limit. I will introduce several non-trivial features of these ``ultrastable’’ states, and discuss some interesting parallels between these states and annealed model glasses.