diff --git a/libcontainer/container_linux.go b/libcontainer/container_linux.go
index 6a91df01db0..613a0eb272e 100644
--- a/libcontainer/container_linux.go
+++ b/libcontainer/container_linux.go
@@ -201,18 +201,30 @@ func (c *Container) Set(config configs.Config) error {
 
 // Start starts a process inside the container. Returns error if process fails
 // to start. You can track process lifecycle with passed Process structure.
-func (c *Container) Start(process *Process) error {
+func (c *Container) Start(process *Process) (retErr error) {
 	c.m.Lock()
-	defer c.m.Unlock()
+	defer func() {
+		if retErr != nil {
+			c.terminate(process)
+		}
+		c.m.Unlock()
+	}()
 	return c.start(process)
 }
 
 // Run immediately starts the process inside the container. Returns an error if
 // the process fails to start. It does not block waiting for the exec fifo
 // after start returns but opens the fifo after start returns.
-func (c *Container) Run(process *Process) error {
+func (c *Container) Run(process *Process) (retErr error) {
 	c.m.Lock()
 	defer c.m.Unlock()
+
+	defer func() {
+		if retErr != nil {
+			c.terminate(process)
+		}
+	}()
+
 	if err := c.start(process); err != nil {
 		return err
 	}
@@ -229,6 +241,34 @@ func (c *Container) Exec() error {
 	return c.exec()
 }
 
+// terminate is to kill the container's init/exec process when got failure.
+func (c *Container) terminate(process *Process) {
+	if process.ops == nil {
+		return
+	}
+	if process.Init {
+		if err := ignoreTerminateErrors(process.ops.terminate()); err != nil {
+			logrus.WithError(err).Warn("unable to terminate initProcess")
+		}
+		// If we haven't saved container's state yet, we need to destroy the
+		// cgroup & intelRdt manager manually.
+		if _, err := os.Stat(filepath.Join(c.stateDir, stateFilename)); os.IsNotExist(err) {
+			if err := c.cgroupManager.Destroy(); err != nil {
+				logrus.WithError(err).Warn("unable to destroy cgroupManager")
+			}
+			if c.intelRdtManager != nil {
+				if err := c.intelRdtManager.Destroy(); err != nil {
+					logrus.WithError(err).Warn("unable to destroy intelRdtManager")
+				}
+			}
+		}
+		return
+	}
+	if err := ignoreTerminateErrors(process.ops.terminate()); err != nil {
+		logrus.WithError(err).Warn("unable to terminate setnsProcess")
+	}
+}
+
 func (c *Container) exec() error {
 	path := filepath.Join(c.stateDir, execFifoFilename)
 	pid := c.initProcess.pid()
@@ -359,12 +399,7 @@ func (c *Container) start(process *Process) (retErr error) {
 				return err
 			}
 
-			if err := c.config.Hooks.Run(configs.Poststart, s); err != nil {
-				if err := ignoreTerminateErrors(parent.terminate()); err != nil {
-					logrus.Warn(fmt.Errorf("error running poststart hook: %w", err))
-				}
-				return err
-			}
+			return c.config.Hooks.Run(configs.Poststart, s)
 		}
 	}
 	return nil
diff --git a/libcontainer/process.go b/libcontainer/process.go
index 3663c7e0dd2..9b25699b8f4 100644
--- a/libcontainer/process.go
+++ b/libcontainer/process.go
@@ -12,6 +12,7 @@ import (
 var errInvalidProcess = errors.New("invalid process")
 
 type processOperations interface {
+	terminate() error
 	wait() (*os.ProcessState, error)
 	signal(sig os.Signal) error
 	pid() int
diff --git a/libcontainer/process_linux.go b/libcontainer/process_linux.go
index 9a2473f716e..55d904f42c7 100644
--- a/libcontainer/process_linux.go
+++ b/libcontainer/process_linux.go
@@ -151,10 +151,6 @@ func (p *setnsProcess) start() (retErr error) {
 			if werr != nil {
 				logrus.WithError(werr).Warn()
 			}
-			err := ignoreTerminateErrors(p.terminate())
-			if err != nil {
-				logrus.WithError(err).Warn("unable to terminate setnsProcess")
-			}
 		}
 	}()
 
@@ -563,16 +559,6 @@ func (p *initProcess) start() (retErr error) {
 			if werr != nil {
 				logrus.WithError(werr).Warn()
 			}
-
-			// Terminate the process to ensure we can remove cgroups.
-			if err := ignoreTerminateErrors(p.terminate()); err != nil {
-				logrus.WithError(err).Warn("unable to terminate initProcess")
-			}
-
-			_ = p.manager.Destroy()
-			if p.intelRdtManager != nil {
-				_ = p.intelRdtManager.Destroy()
-			}
 		}
 	}()