The spontaneous generation of brittle rock damage near and behind the tip of a propagating rupture can produce dynamic feedback mechanisms that modify significantly the rup-ture properties, seismic radiation, and generated fault zone structure. In this work, we study such feedback mechanisms for single rupture events and their consequences for earthquake physics and various possible observations. This is done through numerical simulations of in-plane dynamic ruptures on a frictional fault with bulk behavior governed by a brittle damage rheology that incor-porates reduction of elastic moduli in off-fault yielding regions. The model simulations produce several features that modify key properties of the ruptures, local wave propagation, and fault zone damage. These include (1) dynamic generation of near-fault regions with lower elastic properties, (2) dynamic changes of normal stress on the fault, (3) rupture transition from crack-like to a detached pulse, (4) emergence of a rupture mode consisting of a train of pulses, (5) quasi-periodic modulation of slip rate on the fault, and (6) asymmetric near-fault ground motion with higher amplitude and longer duration on the side with reduced elastic moduli. The results can have significant implications to multiple topics ranging from rupture directivity and local amplification of seismic motion to near-fault tremor-like signals.