Previous investigations have shown that inelastic collapse is a common feature of inelastic, hard-sphere simulations of nondriven (or unforced) flows, provided that the coefficient of restitution is small enough. The focus of the current effort is on a driven system, namely, simple shear flow. Two-dimensional, hard-sphere simulations have been carried out over a considerable range of restitution coefficients (r), solids fractions (nu), and numbers of particles (N). The results indicate that inelastic collapse is an integral feature of the sheared system. Similar to nondriven systems, this phenomenon is characterized by a string of particles engaging in numerous, repeated collisions just prior to collapse. The collapsed string is typically oriented along a 135 degrees angle from the streamwise direction. Inelastic collapse is also found to be more likely in systems with lower r, higher nu, and higher N, as is true for unforced systems. Nonetheless, an examination of the boundary between the collapsed and noncollapsed states reveals that the sheared system is generally more "resistant" to inelastic collapse than its nondriven counterpart. Furthermore, a dimensionless number V* is identified that represents the magnitude of the initial fluctuating velocities relative to that of a characteristic steady-state velocity (i.e., the product of shear rate and particle diameter). For values of V*>>O(1), the transient portion of the simulation is found to be more reminiscent of a nondriven system (i.e., isotropic particle bunching is observed instead of diagonal particle bands).