My understanding is that, in Markov decision processes, absorbing state are states which can transition only to themselves and that these transitions generate rewards of 0. I know that absorbing states are commonly used to represent goals, so an agent might get a non-zero reward when first entering the absorbing state, but all subsequent transitions generate 0 reward (effectively ending the episode).
My question is whether it is appropriate to also represent 'total failure' as an absorbing state. e.g. if the task is for Rabbit to return safely to his burrow (goal state which gives positive reward and ends the episode) while avoiding Fox (failure state which gives negative reward and ends the episode), would both burrow and fox-encounter be absorbing states? If not, how should fox-encounter be represented?