Seismically detectable discontinuities at mid-depths of some cratonic lithospheric mantle define mid-lithosphere discontinuities (MLD), demonstrating that the lithospheric mantle is layered. The genesis and strength of the MLD are still in debate, most proposed models suggest the MLD is likely not weaker than the normal lithosphere, whereas other proposed models suggest that some metasomatised MLD rocks are weaker than the normal lithospheric mantle rocks. Thus, the weak MLD is likely a weakly-coupled layer at mid-depths in some cratonic lithosphere blocks, possibly influencing their stabilities. We assess the geodynamic significance of the MLD using geodynamic modeling. We propose that a weak MLD, with lower effective viscosity, can be connected to thinned cratonic margins during the evolution of some cratons and form continuously connected weak zones from cratonic margins to craton interiors, which can lead to lithospheric thinning or removal by extension, basal drag, delamination, thermochemical erosion, and other actions. Through analyzing different scenarios, we propose that some samples of weak MLDs can be found in a composite ophiolite profile formed on the Precambrian Karelian continental margin, with both continental and oceanic lithosphere, which is supported by chronological, petrological, and structural architectures of the profile. This creates new opportunities to directly study the properties of the MLD, which could help understand and settle the controversies on the origin of the MLD and its physical, chemical, and geophysical properties.