Determining the image of the set of rational points under a morphism of varieties is a very natural and difficult question. The case where the morphism is geometrically surjective has been studied extensively. From Campana's theory of orbifolds, it follows that over a number field, the image of the set of rational points is contained in the set of Campana points for the orbifold base of the morphism. This first approximation of the image of the set of rational points is refined by Abramovich's theory of firmaments. This talk presents a proof of a claim by Abramovich about lifting firm points under toroidal morphisms in joint work with Herr, Mehidi and Poiret.