Mature strike-slip faults are usually surrounded by a narrow zone of damaged rocks characterized by low seismic wave velocities. Observations of earthquakes along such faults indicate that seismicity is highly concentrated within this fault damage zone. However, the long-term influence of the fault damage zone on complete earthquake cycles, i.e., years to centuries, is not well understood. We simulate aseismic slip and dynamic earthquake rupture on a vertical strike-slip fault surrounded by a fault damage zone for a thousand-year timescale using observations along major strike-slip faults, e.g., San Andreas Fault, as constraints on fault zone material properties and geometry. We find that dynamic wave reflections, whose characteristics are strongly dependent on the width and the rigidity contrast of the fault damage zone, have a prominent effect on the stressing history of the fault. The presence of elastic damage can explain, in part, the variability in the earthquake sizes and hypocenter locations along a single fault, which vary with fault damage zone depth, width and rigidity contrast from the host rock. The depth extent of the fault damage zone has a pronounced effect on the earthquake hypocenter locations, and shallower fault damage zones favor shallower hypocenters with a possible bimodal distribution of seismicity along depth. Our findings also suggest significant fault damage zone effects on the hypocenter distribution when the fault damage zone penetrates to the nucleation sites of earthquakes. Therefore the depth distribution of seismicity in mature strike-slip faults is likely influenced by both lithological (material) and rheological (frictional) boundaries.