diff --git a/test/e2e/framework/ginkgowrapper.go b/test/e2e/framework/ginkgowrapper.go
index d8117934831..aa3d6c0a475 100644
--- a/test/e2e/framework/ginkgowrapper.go
+++ b/test/e2e/framework/ginkgowrapper.go
@@ -18,10 +18,36 @@ package framework
 
 import (
 	"path"
+	"reflect"
 
 	"github.com/onsi/ginkgo/v2/types"
+
+	apierrors "k8s.io/apimachinery/pkg/api/errors"
 )
 
+var errInterface = reflect.TypeOf((*error)(nil)).Elem()
+
+// IgnoreNotFound can be used to wrap an arbitrary function in a call to
+// [ginkgo.DeferCleanup]. When the wrapped function returns an error that
+// `apierrors.IsNotFound` considers as "not found", the error is ignored
+// instead of failing the test during cleanup. This is useful for cleanup code
+// that just needs to ensure that some object does not exist anymore.
+func IgnoreNotFound(in any) any {
+	inType := reflect.TypeOf(in)
+	inValue := reflect.ValueOf(in)
+	return reflect.MakeFunc(inType, func(args []reflect.Value) []reflect.Value {
+		out := inValue.Call(args)
+		if len(out) > 0 {
+			lastValue := out[len(out)-1]
+			last := lastValue.Interface()
+			if last != nil && lastValue.Type().Implements(errInterface) && apierrors.IsNotFound(last.(error)) {
+				out[len(out)-1] = reflect.Zero(errInterface)
+			}
+		}
+		return out
+	}).Interface()
+}
+
 // AnnotatedLocation can be used to provide more informative source code
 // locations by passing the result as additional parameter to a
 // BeforeEach/AfterEach/DeferCleanup/It/etc.
diff --git a/test/e2e/framework/internal/unittests/cleanup/cleanup_test.go b/test/e2e/framework/internal/unittests/cleanup/cleanup_test.go
index c47fd14a568..36ed99f12c1 100644
--- a/test/e2e/framework/internal/unittests/cleanup/cleanup_test.go
+++ b/test/e2e/framework/internal/unittests/cleanup/cleanup_test.go
@@ -24,11 +24,13 @@ package cleanup
 import (
 	"context"
 	"flag"
+	"fmt"
 	"regexp"
 	"testing"
 
 	"github.com/onsi/ginkgo/v2"
 
+	metav1 "k8s.io/apimachinery/pkg/apis/meta/v1"
 	"k8s.io/klog/v2"
 	"k8s.io/klog/v2/ktesting"
 	"k8s.io/kubernetes/test/e2e/framework"
@@ -45,10 +47,18 @@ import (
 //
 //
 //
-//
-//
 // This must be line #50.
 
+func init() {
+	framework.NewFrameworkExtensions = append(framework.NewFrameworkExtensions,
+		// This callback runs directly after NewDefaultFramework is done.
+		func(f *framework.Framework) {
+			ginkgo.BeforeEach(func() { framework.Logf("extension before") })
+			ginkgo.AfterEach(func() { framework.Logf("extension after") })
+		},
+	)
+}
+
 var _ = ginkgo.Describe("e2e", func() {
 	ginkgo.BeforeEach(func() {
 		framework.Logf("before")
@@ -85,22 +95,21 @@ var _ = ginkgo.Describe("e2e", func() {
 		ginkgo.DeferCleanup(func() {
 			framework.Logf("cleanup first")
 		})
+
+		ginkgo.DeferCleanup(framework.IgnoreNotFound(f.ClientSet.CoreV1().PersistentVolumes().Delete), "simple", metav1.DeleteOptions{})
+		fail := func(ctx context.Context, name string) error {
+			return fmt.Errorf("fake error for %q", name)
+		}
+		ginkgo.DeferCleanup(framework.IgnoreNotFound(fail), "failure")
+
+		// More test cases can be added here without affeccting line numbering
+		// of existing tests.
 	})
 })
 
-func init() {
-	framework.NewFrameworkExtensions = append(framework.NewFrameworkExtensions,
-		// This callback runs directly after NewDefaultFramework is done.
-		func(f *framework.Framework) {
-			ginkgo.BeforeEach(func() { framework.Logf("extension before") })
-			ginkgo.AfterEach(func() { framework.Logf("extension after") })
-		},
-	)
-}
-
 const (
 	ginkgoOutput = `[BeforeEach] e2e
-  cleanup_test.go:53
+  cleanup_test.go:63
 INFO: before
 [BeforeEach] e2e
   set up framework | framework.go:xxx
@@ -109,30 +118,34 @@ INFO: >>> kubeConfig: yyy/kube.config
 STEP: Building a namespace api object, basename test-namespace
 INFO: Skipping waiting for service account
 [BeforeEach] e2e
-  cleanup_test.go:95
+  cleanup_test.go:56
 INFO: extension before
 [BeforeEach] e2e
-  cleanup_test.go:61
+  cleanup_test.go:71
 INFO: before #1
 [BeforeEach] e2e
-  cleanup_test.go:65
+  cleanup_test.go:75
 INFO: before #2
 [It] works
-  cleanup_test.go:80
+  cleanup_test.go:90
 [AfterEach] e2e
-  cleanup_test.go:96
+  cleanup_test.go:57
 INFO: extension after
 [AfterEach] e2e
-  cleanup_test.go:69
+  cleanup_test.go:79
 INFO: after #1
 [AfterEach] e2e
-  cleanup_test.go:76
+  cleanup_test.go:86
 INFO: after #2
 [DeferCleanup (Each)] e2e
-  cleanup_test.go:85
+  cleanup_test.go:103
+[DeferCleanup (Each)] e2e
+  cleanup_test.go:99
+[DeferCleanup (Each)] e2e
+  cleanup_test.go:95
 INFO: cleanup first
 [DeferCleanup (Each)] e2e
-  cleanup_test.go:82
+  cleanup_test.go:92
 INFO: cleanup last
 [DeferCleanup (Each)] e2e
   dump namespaces | framework.go:xxx
@@ -187,6 +200,10 @@ func TestCleanup(t *testing.T) {
 			Name:            "e2e works",
 			NormalizeOutput: normalizeOutput,
 			Output:          ginkgoOutput,
+			// It would be nice to get the cleanup failure into the
+			// output, but that depends on Ginkgo enhancements:
+			// https://github.com/onsi/ginkgo/issues/1041#issuecomment-1274611444
+			Failure: `DeferCleanup callback returned error: fake error for "failure"`,
 		},
 	}