Proper wound healing necessitates both coagulation (the formation of a blood clot) and fibrinolysis (the dissolution of a blood clot). A thrombus resistant to clot dissolution can obstruct blood flow, leading to vascular pathologies. This study seeks to understand the mechanisms by which individual fibrin fibers, the main structural component of blood clots, are cleared from a local volume during fibrinolysis. We observed 2-D fibrin networks during lysis by plasmin, recording the clearance of each individual fiber. We found that, in addition to transverse cleavage of fibers, there were multiple other pathways by which clot dissolution occurred, including fiber bundling, buckling, and collapsing. These processes are all influenced by concentration of plasmin utilized in lysis. The network fiber density influenced the kinetics and distribution of these pathways. Individual cleavage events often resulted in large morphological changes in network structure, suggesting that the inherent tension in fibers played a role in fiber clearance. Using images before and after a cleavage event to measure fiber lengths, we estimated that fibers are strained ~23% beyond their equilibrium length during polymerization. To understand the role of fiber tension in fibrinolysis we modeled network clearance under differing amounts of fiber polymerized strain (prestrain). The comparison of experimental and model data indicated that fibrin tension enables 35% more network clearance due to network rearrangements after individual cleavage events than would occur if fibers polymerized in a non-tensed state. Our results highlight many characteristics and mechanisms of fibrin breakdown, which have implications on future fibrin studies, our understanding of the fibrinolytic process, and the development of thrombolytic therapies.