Distributed services are often provided by process groups for purposes of reliability, availability, and performance. It is often important for the members of such a group to have a consistent view of the group's membership. For this reason, membership services are important part of many distributed software systems. Despite their importance, the specification and implementation of membership services in completely asynchronous systems has challenged researchers. Recent papers have demonstrated that earlier specifications are either unsolvable or admit trivial solutions. Informally, membership services require a kind of agreement among processes and it has been shown that it is impossible to solve many consensus-like problems in completely asynchronous systems. If the specification of membership service is nearly that strong as that of consensus, the specification will be unsolvable. If it is much weaker, its solution may be useless. This paper provides an alternative specification of group membership and exhibits an algorithm that satisfies it. The specification is solvable in spite of earlier impossibility results because it permits executions in which all processes are evicted from the process group yet none ever learns that the group has become empty. This represents a weakening of earlier specifications, which required that, at all times, at least one process be aware of a group's membership. However, the new specification cannot be trivially satisfied because it prohibits a potential solution from arbitrarily removing a process for no reason. This specification thus represents an important step towards a better understanding of membership services in completely asynchronous systems.