A Finite Element (FE) model is developed with a commercial code, to investigate the keyhole dynamics and stability at keyhole threshold, a fusion regime characteristic to laser micro-welding or to Laser Powder Bed Fusion (LPBF). The model includes relevant physics to treat the hydrodynamic problemsurface tension, Marangoni stress and recoil pressure-as well as a self-consistent ray-tracing algorithm to account for the "beam-trapping" effect. Implemented in both static and scanning laser configurations, the model successfully reproduces some key features that most recent x-ray images have exhibited. The dynamics of the liquid/gas interface is analyzed, in line with the distribution of the absorbed intensity as well as with the increase of the keyhole energy coupling. Based on these results, new elements are provided to discuss our current understanding of the keyhole formation and stability at threshold.