Abstract: The paper dispels the myth that it is impossible for any stabilizing message-passing program to be terminating. We identify fixpoint-symmetry as a necessary condition for a message-passing stabilizing program to be terminating. Our results do confirm that a number of well-known input-output problems (e.g., leader election and consensus) do not admit a terminating and stabilizing solution. On the flip side, they show that reactive problems such as mutual exclusion and reliable-transmission do admit such solutions. We go on to present stabilizing and terminating programs for both problems. Also, we describe a way to add termination to a stabilizing program, and demonstrate it in the context of our design of a solution to the reliable- transmission problem.