We consider chemical reaction networks operating on discrete state spaces, i.e., where we keep track of molecule counts. We give a sufficient syntactic condition on chemical reaction networks for the impossibility of certain reactions to take place in the long term. This result is a statement about the reachability relation and is therefore independent of stochastics. As such, it can equivalently be formulated in terms of Petri nets, which is a well-studied model of concurrency.