Seismic velocity changes in earthquake cycles have been observed over a wide range of timescales and may be a good indicator of the onset of future earthquakes. Understanding the effects of precursory velocity changes right before seismic and slow-slip events could potentially elucidate the onset and timing of fault failure. We use numerical models to simulate fully dynamic earthquake cycles in 2D strike-slip fault systems with antiplane geometry, surrounded by a narrow fault-parallel damage zone. By imposing S-wave velocity changes inside fault damage zones, we investigate the effects of these precursors on multiple stages of the seismic cycle, including nucleation, coseismic, postseismic, and interseismic stages. Our modeling results show a wide spectrum of fault slip behaviors including fast earthquakes, slow-slip events, and variable creep. One primary effect of the imposed velocity precursor is on the earthquake nucleation phase, and earlier onset of precursors causes earthquakes to nucleate sooner with a smaller nucleation size that is not predicted by theoretical equations. Furthermore, such precursors affect the nucleation of dynamic earthquakes and slow-slip events. Our results highlight the importance of short- and long-term monitoring of fault zone structures for better assessment of regional seismic hazard.