diff --git a/e2e/container/run_test.go b/e2e/container/run_test.go
index fa8ea72b03..d4fea81769 100644
--- a/e2e/container/run_test.go
+++ b/e2e/container/run_test.go
@@ -1,8 +1,10 @@
 package container
 
 import (
+	"bytes"
 	"fmt"
 	"strings"
+	"syscall"
 	"testing"
 	"time"
 
@@ -13,6 +15,7 @@ import (
 	is "gotest.tools/v3/assert/cmp"
 	"gotest.tools/v3/golden"
 	"gotest.tools/v3/icmd"
+	"gotest.tools/v3/poll"
 	"gotest.tools/v3/skip"
 )
 
@@ -221,3 +224,26 @@ func TestMountSubvolume(t *testing.T) {
 		})
 	}
 }
+
+func TestProcessTermination(t *testing.T) {
+	var out bytes.Buffer
+	cmd := icmd.Command("docker", "run", "--rm", "-i", fixtures.AlpineImage,
+		"sh", "-c", "echo 'starting trap'; trap 'echo got signal; exit 0;' TERM; while true; do sleep 10; done")
+	cmd.Stdout = &out
+	cmd.Stderr = &out
+
+	result := icmd.StartCmd(cmd).Assert(t, icmd.Success)
+
+	poll.WaitOn(t, func(t poll.LogT) poll.Result {
+		if strings.Contains(result.Stdout(), "starting trap") {
+			return poll.Success()
+		}
+		return poll.Continue("waiting for process to trap signal")
+	}, poll.WithDelay(1*time.Second), poll.WithTimeout(5*time.Second))
+
+	assert.NilError(t, result.Cmd.Process.Signal(syscall.SIGTERM))
+
+	icmd.WaitOnCmd(time.Second*10, result).Assert(t, icmd.Expected{
+		ExitCode: 0,
+	})
+}