There is a failure detection mechanism provided that is able to find and report which servers are silent and as such assumed to be dead. At a high level, the failure detector is a distributed service that provides information about which servers may be dead (suspicions). Later if the group agrees that the suspicions are probably true, then the group decides that a given server has indeed failed. This means that the remaining members in the group take a coordinated decision to exclude a given member.
Suspicions are triggered when servers go mute. When server A does not receive messages from server B during a given period, a timeout occurs and a suspicion is raised.
If a server gets isolated from the rest of the group, then it suspects that all others have failed. Being unable to secure agreement with the group (as it cannot secure a quorum), its suspicion does not have consequences. When a server is isolated from the group in this way, it is unable to execute any local transactions.