The nuclear lamina, composed of intermediate filaments, is a structural protein meshwork at the nuclear membrane that protects genetic material and regulates gene expression.Here we uncover the physical basis of the material design of nuclear lamina that enables it to withstand extreme mechanical deformation of >100% strain despite the presence of structural defects. Through a simple in silico model we demonstrate that this is due to nanoscale mechanisms including protein unfolding, alpha-to-beta transition, and sliding, resulting in a characteristic nonlinear force-extension curve. At the larger microscale this leads to an extreme delocalization of mechanical energy dissipation, preventing catastrophic crack propagation. Yet, when catastrophic failure occurs under extreme loading, individual protein filaments are sacrificed rather than the entire meshwork. This mechanism is theoretically explained by a characteristic change of the tangent stress-strain hardening exponent under increasing strain. Our results elucidate the large extensibility of the nuclear lamina within muscle or skin tissue and potentially many other protein materials that are exposed to extreme mechanical conditions, and provide a new paradigm toward the de novo design of protein materials by engineering the nonlinear stress-strain response to facilitate flaw-tolerant behavior.