In this project, we propose to determine, in a way independent of stellar evolution and its associated uncertainties, the radial stratification of carbon/oxygen in the cores of evolved low mass stars. This concerns both the helium burning horizontal branch stars and the white dwarf stage. The carbon/oxygen stratification in the core of evolved low-mass stars results from various physical phenomena occurring during the late stages of the evolution of stars. We expect this stratification to be shaped, over time, by the helium flash, convection, overshooting and semi-convection in the helium burning cores, possible additional mixing factors (due to rotation for instance), AGB and post-AGB He burning shell evolution, and the somewhat uncertain rate of the 12C(alpha,gamma)16O nuclear reaction. All these notoriously suffer from serious uncertainties and are not securely modeled in current stellar evolution codes. Particularly revealing is that each code available today on the market to model the late phases of evolution predicts a C/O stratification in the cores of white dwarf stars that differ substantially, and there is presently no way to affirm that one code provides more realistic results than the others on that point (indeed, most likely none provides the real stratification in these stars). This unfortunate situation seriously limits progress in our knowledge of the ultimate phases of stellar evolution, with damaging consequences for other fields. For this project, our main "laboratories" will be the hot B subdwarf stars, burning helium in their cores, that represent an intermediate stage of stellar evolution (the horizontal branch) and the white dwarf stars that constitute the ultimate stage for the vast majority of stars in the Universe. Both sdB and white dwarf stars are known to develop nonradial oscillations with deep probing g-modes that provide means to access the core of these stars through asteroseismology. Deriving their internal C/O profiles will pose strong constraints on key processes in stellar physics that shape this stratification over time. It is also important for dating old galactic structures with white dwarf cosmochronology, a method that will certainly experience a renewed interest in a near future as the GAIA mission will soon deliver its data. This project therefore represents a key challenge with strong repercussions expected on stellar physics and other fields of astrophysics.