diff --git a/test/e2e/node/pods.go b/test/e2e/node/pods.go
index b4e1ba160c7..ae458f036ef 100644
--- a/test/e2e/node/pods.go
+++ b/test/e2e/node/pods.go
@@ -1015,6 +1015,11 @@ func (v *podStartVerifier) Verify(event watch.Event) error {
 		switch {
 		case t.ExitCode == 1:
 			// expected
+		case t.ExitCode == 2 && t.Reason == "Error" && t.Message == "":
+			// Some runtimes occasionally surface exit code 2 if stopped before execve makes
+			// it to launching /bin/false in fast-delete scenarios. The test only cares
+			// that the container failed.
+			framework.Logf("pod %s on node %s failed with the symptoms of https://github.com/kubernetes/kubernetes/issues/135713", pod.Name, pod.Spec.NodeName)
 		case t.ExitCode == 137 && (t.Reason == "ContainerStatusUnknown" || t.Reason == "Error"):
 			// expected, pod was force-killed after grace period
 		case t.ExitCode == 128 && (t.Reason == "StartError" || t.Reason == "ContainerCannotRun") && reBug88766.MatchString(t.Message):