Tectonic faults typically break in a single rupture mode within the range of styles from slow slip to dynamic earthquake failure. However, in increasingly well-documented instances, the same fault segment fails in both slow and fast modes within a short period, as in the sequences that culminated in the 2011 Mw = 9.0 Tohoku-Oki, Japan, and 2014 Mw = 8.2 Iquique, Chile, earthquakes. Why slow slip alternates with dynamic rupture in certain regions but not in others is not well understood. Here, we integrate laboratory experiments and numerical simulations to investigate the physical conditions leading to cycles where the two rupture styles alternate. We show that a bifurcation takes place near the stability transition with sequences encompassing various rupture modes under constant loading rate. The range of frictional instabilities and slip cycles identified in this study represents important end-members to understand the interaction of slow and fast slip on the same fault segment. Plain Language Summary Earthquake faults fail in a range of different modes depending on the tectonic setting. The northern Cascadia and the Nankai regions produce irregular slow-slip events whereas Japan, Chile, and the Middle American subduction zones have shown that both slow slip and ordinary (fast) earthquakes can occur in a single location. Why only slow slip appears in certain regions but transitions to fast ruptures in others is not fully understood. Using laboratory experiments and numerical simulations, we show that both fast and slow failure can occur when the fault is only weakly unstable. Under these conditions faults fail with a range of slip velocities, dictated by fault friction. Describing the dynamics of frictional sliding near the stability transition in controlled experiments helps us better characterize the evolution of seismic hazards in a natural setting.