Even though polycrystalline graphene has shown a surprisingly high tensile strength, the influence of inherent grain boundaries on such property remains unclear. We study the fracture properties of a series of polycrystalline graphene models of increasing thermodynamic stability, as obtained from a long molecular dynamics simulation at an elevated temperature. All of the models show the typical and well-documented brittle fracture behavior of polycrystalline graphene; however, a clear decrease in all fracture properties is observed with increasing annealing time. The remarkably high fracture properties obtained for the most disordered (less annealed) structures arise from the formation of many nonpropagating prefracture cracks, significantly retarding failure. The stability of these reversible cracks is due to the nonlocal character of load transfer after a bond rupture in very disordered systems. It results in an insufficient strain level on neighboring bonds to promote fracture propagation. Although polycrystallinity seems to be an unavoidable feature of chemically synthesized graphenes, these results suggest that targeting highly disordered states might be a convenient way to obtain improved mechanical properties.