Duality ideas connect irreducible Markov chains with absorbing ones, but there are other ways of building relations between these two classes of processes. In this talk, we will discuss two other connections between these models when time goes to infinity. In the first one, we will make a correspondence between a specific irreducible model associated with a given absorbing one, allowing to derive results for which we will show applications. One of them lead to the second type of connection, where we will show relations in absorbing chains corresponding to balance of the probabilistic flux across cuts in irreducible stationary models. As in the latter case, where these balance equations are helpful in deriving equilibrium distributions, we will show how using the corresponding relations in the former case leads to simplifications in computations on absorbing models.