Discrete element simulations are employed to study the influence of static friction on the mechanical response of assemblies of nonbonded semiflexible fibers during cycles of isostatic compressions and releases. Hysteresis is evidenced during the cycles and is related to the sensitivity of the frictional contacts on normal forces. Nonzero frictions are shown to decrease both the packing density and caging number but do not affect the critical exponents that characterize the pressure and bulk and shear moduli. Assemblies of frictionless fibers are found fragile in the sense that they resist isostatic compressions but have a zero shear modulus at all densities.