Group Replication includes a failure detection mechanism 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). 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. 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 expel a given member.
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.
Where the network is unstable and members frequently lose and regain connection to each other in different combinations, it is theoretically possible for a group to end up marking all its members for expulsion, after which the group would cease to exist and have to be set up again. To counter this possibility, from MySQL 8.0.20, Group Replication's Group Communication System (GCS) tracks the group members that have been marked for expulsion, and treats them as if they were in the group of suspected members when deciding if there is a majority. This ensures at least one member remains in the group and the group can continue to exist. When an expelled member has actually been removed from the group, GCS removes its record of having marked the member for expulsion, so that the member can rejoin the group if it is able to.
For information on the Group Replication system variables that you can configure to specify the responses of working group members to failure situations, and the actions taken by group members that are suspected of having failed, see Section 18.7.7, “Responses to Failure Detection and Network Partitioning”.