Using triaxial numerical experiments, we investigated the evolution of the state of stress and that of the bulk instantaneous and finite strain during ongoing convergence and subsequent progressive tectonic unloading of a warm and buoyant continental lithosphere. Various unloading histories of the driving tectonic force were considered. As the tectonic force progressively declines, the instantaneous strain evolves from plane strain to horizontal constriction in a direction perpendicular to that of convergence, and finally to horizontal flattening. During the progressive unloading of the tectonic force driving convergence, bulk constrictional strain accommodates the release of accumulated gravitational stress. The decline of the triaxial strain rates to low values reduces the potential for the orogen-parallel linear fabric to be erased by horizontal flattening. This is confirmed by the finite strain ellipsoid that evolves toward plane strain with a long axis parallel to the orogen. In the ca. 2.5 Ga Gawler and Terre Adélie cratons, we have identified a well-preserved and widespread horizontal linear fabric. As suggested by our numerical experiments, we associate the development of this linear fabric with the waning stages of late Archean convergence.