Cratons are regions of the Earth's crust that have been relatively stable for more than a couple of billion years. This stability is remarkable — the strong tectonic plates in the ocean are, after all, recycled into the deep mantle in less than a tenth of this time.

In Figure 1, the cratons are marked as blue patches of thick lithosphere. The question of their stability is still open: it surely has to do with the thick, strong and buoyant lithosphere but is that enough to guarantee a billion year lifespan ? It is also a puzzle to work out how the Earth could make lithosphere that is as strong and buoyant as this and not be able to destroy it again.

Figure 1 from Cooper et al, 2020 - This map shows deep seismicity (bright coloured dots trending from red to dark blue as the source becomes deeper), the relative thickness of the crust and lithosphere which is a proxy for overall strength (darker is weaker) and, in blue patches, the regions where the lithosphere is more than 250km thick. 

The work of Cooper, Farrington and Miller shows that mantle flow driven by nearby slabs and focused by the presence of the thick cratonic lithosphere can trim away the weaker parts of the craton margin and leave a stronger, steeper edge in the deep lithosphere. This is one way to understand how the most destructive elements in the Earth's deep circulation, subducting slabs, can also be responsible for the development of long-lived stable structures.

We propose that subducting slabs may cause lithospheric removal by directing mantle flow along the craton margin. This process could carve and shape the cratons, leading to conditions that impact the overall (in)stability of the lithosphere. We use three-dimensional geodynamic models to investigate how subduction-driven directed flow interacts with cratonic lithosphere of differing shape, concluding that the margin shape controls both channeliza- tion of flow around the craton as well as the potential for destruction. While the simulations show that all craton shapes aid in channelization, the cratons with straight vertical margins are the most resistant to deformation, and the cratons with gradually thickening margins are less resistant to deformation. The dependence on shape could contribute to the progressive removal of cratonic lithosphere along its margin in a runaway process until a more stable vertical margin shape evolves

Cooper, C.M., R.J. Farrington, and M.S. Miller. “On the Destructive Tendencies of Cratons.” Geology, October 7, 2020.

In a recent seminar, Katie Cooper gives a thorough overview of the nature of cratonic lithosphere, thoughts on why it is stable and a detailed explanation of this paper.

Seminar on this topic (and more) by the lead author, Katie Cooper, WSU. 

A discussion on Craton stability and formation

Craton Formation and the Onset of Plate Tectonics
Cratons are anomalously-strong regions of the continents that have largely resisted tectonic forces for billions of years. How such strong…
A related article that includes background reading on plate tectonics and cratons. (Beall, A. P., L. Moresi, and C. M. Cooper. “Formation of Cratonic Lithosphere during the Initiation of Plate Tectonics.” Geology 46, no. 6 (June 1, 2018): 487–90.