Dry granular materials, such as sand, gravel, pills, or agricultural grains, can become rigid when compressed or sheared. Under isotropic compression, the material reaches a certain jamming density and then resists further compression. Shear jamming occurs when resistance to shear emerges in a system at a density lower than the jamming density. Although shear jamming is prevalent in frictional granular materials, their stability properties are not well described by standard elasticity theory and thus call for experimental characterization. We report on experimental observations of changes in the mechanical properties of a shear-jammed granular material subjected to small-amplitude, quasistatic cyclic shear. We study a layer of plastic disks confined to a shear cell, using photoelasticimetry to measure all interparticle vector forces. For sufficiently small cyclic shear amplitudes and large enough initial shear, the material evolves to an unexpected “ultrastable” state in which all the particle positions and interparticle contact forces remain unchanged after each complete shear cycle for thousands of cycles. The stress response of these states to small imposed shear is nearly elastic, in contrast to the original shear-jammed state.