diff --git a/daemon/monitor.go b/daemon/monitor.go
index 9a087283c8..d0df021e28 100644
--- a/daemon/monitor.go
+++ b/daemon/monitor.go
@@ -148,7 +148,7 @@ func (daemon *Daemon) ProcessEvent(id string, e libcontainerdtypes.EventType, ei
 
 		daemon.LogContainerEvent(c, "oom")
 	case libcontainerdtypes.EventExit:
-		if int(ei.Pid) == c.Pid {
+		if ei.ProcessID == libcontainerdtypes.InitProcessName {
 			return daemon.handleContainerExit(c, &ei)
 		}
 
diff --git a/libcontainerd/remote/client.go b/libcontainerd/remote/client.go
index 5278d4a974..d88629affe 100644
--- a/libcontainerd/remote/client.go
+++ b/libcontainerd/remote/client.go
@@ -674,7 +674,7 @@ func (c *client) processEvent(ctx context.Context, et libcontainerdtypes.EventTy
 			}).Error("failed to process event")
 		}
 
-		if et == libcontainerdtypes.EventExit && ei.ProcessID != ei.ContainerID {
+		if et == libcontainerdtypes.EventExit && ei.ProcessID != libcontainerdtypes.InitProcessName {
 			p, err := c.getProcess(ctx, ei.ContainerID, ei.ProcessID)
 			if err != nil {
 
@@ -823,6 +823,9 @@ func (c *client) processEventStream(ctx context.Context, ns string) {
 					ExitCode:    t.ExitStatus,
 					ExitedAt:    t.ExitedAt,
 				}
+				if t.ID == t.ContainerID {
+					ei.ProcessID = libcontainerdtypes.InitProcessName
+				}
 			case *apievents.TaskOOM:
 				et = libcontainerdtypes.EventOOM
 				ei = libcontainerdtypes.EventInfo{