This should be fairly standard, but I fail to google it, and nothing on the matter is on Math.SE.
How do we call the opposite of an absorbing state? If we think about Markov chains/systems, that would be a state such that there is no positive transition probability to that state from any other one.
In other words, a state that - if we didn't start in it - we would never end up in it.
In the context of finite state automata, such states are called Garden of Eden states.
E.F. Moore proved existence of such states of certain infinite automata in Machine models of self-reproduction, Proc. Sympos. Appl. Math., Vol. 14, pp. 17-34 (1963). See Amorosa and Cooper (1970) for some extensions to finite configurations.
Moore attributed the name to John Tukey in the 1950's.