What geological processes would 'restart' subduction processes?
Subduction is ultimately driven by the heat flow process of mantle convection. A mantle plume beneath a stable plate will ultimately cause that plate to split, a la the African rift zone we observe today. 

The crust of the earth is very thin compared to the mass of flowing material beneath it. As my global geophysics prof taught us, the fact that the earth has a solid outer "skin" is a consequence of the thermal conditions around the earth's surface and geochemistry, but that has little to no effect on the thermal conditions within the planet that ultimately control thermal convection that expresses itself on the surface as plate motions. I.E., the thermal mass of the crust is inconsequential when considering the thermal mechanisms that drive the mantle and outer core. Heat makes the plate go! 

On the surface, plates may move, be created or destroyed, but thermodynamics tells us these are consequences, not drivers. We may observe evidence of past situations where plates appear to be static with respect to the underlying mantle motions, but this does not reveal any new mechanism that would suggest plate tectonic theory would not predict such circumstances.