Instabilities and failure in ductile non associated materials have been widely investigated during last decades especially in the case of geomaterials. It has been experimentally proved that collapse of some sample can occur strictly within the ultimate plasticity limit as characterized experimentally. From a theoretical point of view such instability problems are well described using the so called second order work criterion derived from the Hill's stability analysis \cite{HIL_58}. Hence a question arises as to the experimental characterisation of the ultimate plasticity limit and its uniqueness with respect to the choice of stress paths. After a few reminders on Hill's theory, we prove in a general framework that the drained triaxial paths allow to determine with certainty this ultimate plasticity limit without any risk of preliminary bifurcation whatever the elasto-plastic material considered. We also conclude that this plasticity limit can be considered as unique because it depends mainly on the initial reference configuration of the material and not so much on the texture anisotropy that develops during the loading path. Furthermore, we define the limit of the bifurcation domain as the surface drawn in the 6-dimensional stress space that delimits the unconditionally stable space from the one where instabilities and failures can occur within the plasticity limit. We show, however, that this last limit is itself very sensitive to the evolution of this texture anisotropy and evolves continuously with the loading path. Thus it can be not considered as unique.