ESXi fails - VMware HA will restart the VMs running on the failed host on the other hosts in the HA cluster
ESXi is powered off - since this is intiated by an administrator the VM will have to be placed in Maintenance mode requiring the VMs to migrated off or shut down before the host can be powered off -
Network failure - with a network failure the ESXi host become isolated from the HA Cluster - and you can configure what that node does in this situattion - either leave the VMs running which assumes that connectivity to the VMs is not affected or power the VMs down which will allow the VMs to be restarted on the remaining hosts in the cluster -
Follow Duncan's suggestions for your HA settings -