Replicative senescence (RS) that limits the proliferating potential of normal eukaryotic cells occurs either by a cell-division counting mechanism linked to telomere erosion or prematurely through induction by cell stressors such as oncogene hyper-activation. However, there is evidence that RS also occurs by a stochastic process that is independent of number of cell divisions or cellular stress and yet it leads to a highly-stable, non-reversible post-mitotic state that may be long-lasting and that such a process is widely represented among higher eukaryotes. Here I present and discuss evidence that the interactions between DNA and the nuclear substructure, commonly known as the nuclear matrix, define a higher-order structure within the cell nucleus that following thermodynamic constraints, stochastically evolves towards maximum stability, thus becoming limiting for mitosis to occur. It is suggested that this process is responsible for ultimate replicative senescence and yet it is compatible with long-term cell survival.