Fibrin is an elastomeric protein forming highly extensible fiber networks that provide the scaffold of blood clots. Here we reveal the molecular mechanisms that explain the large extensibility of fibrin networks by performing in situ small angle X-ray scattering measurements while applying a shear deformation. We simultaneously measure shear-induced alignment of the fibers and changes in their axially ordered molecular packing structure. We show that fibrin networks exhibit distinct structural responses that set in consecutively as the shear strain is increased. They exhibit an entropic response at small strains (<5%), followed by progressive fiber alignment (>25% strain) and finally changes in the fiber packing structure at high strain (>100%). Stretching reduces the fiber packing order and slightly increases the axial periodicity, indicative of molecular unfolding. However, the axial periodicity changes only by 0.7%, much less than the 80% length increase of the fibers, suggesting that fiber elongation mainly stems from uncoiling of the natively disordered αC-peptide linkers that laterally bond the molecules. Upon removal of the load, the network structure returns to the original isotropic state, but the fiber structure becomes more ordered and adopts a smaller packing periodicity compared to the original state. We conclude that the hierarchical packing structure of fibrin fibers, with built-in disorder, makes the fibers extensible and allows for mechanical annealing. Our results provide a basis for interpreting the molecular basis of haemostatic and thrombotic disorders associated with clotting and provide inspiration to design resilient bio-mimicking materials. Statement of Significance: Fibrin provides structural integrity to blood clots and is also widely used as a scaffold for tissue engineering. To fulfill their biological functions, fibrin networks have to be simultaneously compliant like skin and resilient against rupture. Here, we unravel the structural origin underlying this remarkable mechanical behaviour. To this end, we performed in situ measurements of fibrin structure across multiple length scales by combining X-ray scattering with shear rheology. Our findings show that fibrin sustains large strains by undergoing a sequence of structural changes on different scales with increasing strain levels. This demonstrates new mechanistic aspects of an important biomaterial's structure and its mechanical function, and serves as an example in the design of biomimicking materials.