The emerging generation of robots composed of soft materials strives to match biological motor adaptation skills via shape-shifting. Soft robots often harness volumetric expansion directed by strain limiters to deform in complex ways. Traditionally, strain limiters have been inert materials embedded within a system to prescribe a single deformation. Under changing task demands, a fixed deformation mode limits adaptability. Recent technologies for on-demand reprogrammable deformation of soft bodies, including thermally activated variable stiffness materials and jamming systems, presently suffer from long actuation times or introduce unwanted bending stiffness. We present fibers that switch tensile stiffness via jamming of segmented elastic fibrils. When jammed, tensile stiffness increases more than 20× in less than 0.1 s, but bending stiffness increases only 2×. When adhered to an inflating body, jamming fibers locally limit surface tensile strains, unlocking myriad programmable deformations. The proposed jamming technology is scalable, enabling adaptive behaviors in emerging robotic materials that interact with unstructured environments.