When a client disconnects/unpossesses a mover character, the character's Network Prediction Component will re-configure itself now that it does not have a net connection. However, this handling will not be performed if the server's only client disconnects.
FNetworkPredictionProxy::InitForNetworkRole is called from UNetworkPredictionComponent::CheckOwnerRoleChange, and this is checked each update during UNetworkPredictionComponent::PreReplication.
However, if the server no longer has any client connections, it won't call into UNetDriver::ServerReplicateActors_BuildConsiderList, where actors considered for replication will call PreReplication. Because of this, UNetworkPredictionWorldManager::ConfigureInstance is not called with the updated values for Role/bHasNetConnection, configuring it to be locally controlled.