Many natural structures use a foam core and solid outer shell to achieve high strength and stiffness with relatively small amounts of mass. Biological foams, however, must also resist crack growth. The process of crack propagation within the struts of a foam is not well understood and is complicated by the foam microstructure. We demonstrate that in cancellous bone, the foam-like component of whole bones, damage propagation during cyclic loading is dictated not by local tissue stresses but by heterogeneity of material properties associated with increased ductility of strut surfaces. The increase in surface ductility is unexpected because it is the opposite pattern generated by surface treatments to increase fatigue life in man-made materials, which often result in reduced surface ductility. We show that the more ductile surfaces of cancellous bone are a result of reduced accumulation of advanced glycation end products compared with the strut interior. Damage is therefore likely to accumulate in strut centers making cancellous bone more tolerant of stress concentrations at strut surfaces. Hence, the structure is able to recover more deformation after failure and return to a closer approximation of its original shape. Increased recovery of deformation is a passive mechanism seen in biology for setting a broken bone that allows for a better approximation of initial shape during healing processes and is likely the most important mechanical function. Our findings suggest a previously unidentified biomimetic design strategy in which tissue level material heterogeneity in foams can be used to improve deformation recovery after failure.