A primary objective of relativistic cosmology has long been to encode the apparent isotropy in our universe and its evolution in a mathematical formulation. Quiescent cosmology ? a school of thought for the explanation of the large-scale isotropy - already possesses a mathematical framework, namely the definition of an isotropic singularity, but only for the initial state of the universe. A complementary framework is therefore necessary to also describe possible final states of the universe. Our new definitions of an anisotropic future endless universe and an anisotropic future singularity, whose conformal structure and properties differ significantly from those of the isotropic singularity, offer a promising realisation for this framework. The combination of the three definitions together could then provide the first complete formalisation of the quiescent cosmology concept.