diff --git a/pkg/executor/executor_failpoint_test.go b/pkg/executor/executor_failpoint_test.go
index 027181293c73b..031acf115bd40 100644
--- a/pkg/executor/executor_failpoint_test.go
+++ b/pkg/executor/executor_failpoint_test.go
@@ -360,6 +360,25 @@ func TestCoprocessorOOMTiCase(t *testing.T) {
 	*/
 }
 
+func TestCoprocessorBlockIssues56916(t *testing.T) {
+	store := testkit.CreateMockStore(t)
+	tk := testkit.NewTestKit(t, store)
+	require.NoError(t, failpoint.Enable("github.com/pingcap/tidb/pkg/store/copr/issue56916", `return`))
+	defer func() { require.NoError(t, failpoint.Disable("github.com/pingcap/tidb/pkg/store/copr/issue56916")) }()
+
+	tk.MustExec("use test")
+	tk.MustExec("drop table if exists t_cooldown")
+	tk.MustExec("create table t_cooldown (id int auto_increment, k int, unique index(id));")
+	tk.MustExec("insert into t_cooldown (k) values (1);")
+	tk.MustExec("insert into t_cooldown (k) select id from t_cooldown;")
+	tk.MustExec("insert into t_cooldown (k) select id from t_cooldown;")
+	tk.MustExec("insert into t_cooldown (k) select id from t_cooldown;")
+	tk.MustExec("insert into t_cooldown (k) select id from t_cooldown;")
+	tk.MustExec("split table t_cooldown by (1),(2),(3),(4),(5),(6),(7),(8),(9),(10);")
+	tk.MustQuery("select * from t_cooldown use index(id) where id > 0 and id < 10").CheckContain("1")
+	tk.MustQuery("select * from t_cooldown use index(id) where id between 1 and 10 or id between 124660 and 132790;").CheckContain("1")
+}
+
 func TestIssue21441(t *testing.T) {
 	require.NoError(t, failpoint.Enable("github.com/pingcap/tidb/pkg/executor/union/issue21441", `return`))
 	defer func() {
diff --git a/pkg/store/copr/coprocessor.go b/pkg/store/copr/coprocessor.go
index f3dd58c911ce5..085dfbe350779 100644
--- a/pkg/store/copr/coprocessor.go
+++ b/pkg/store/copr/coprocessor.go
@@ -223,6 +223,12 @@ func (c *CopClient) BuildCopIterator(ctx context.Context, req *kv.Request, vars
 		it.concurrency = 1
 	}
 
+	// issue56916 is about the cooldown of the runaway checker may block the SQL execution.
+	failpoint.Inject("issue56916", func(_ failpoint.Value) {
+		it.concurrency = 1
+		it.smallTaskConcurrency = 0
+	})
+
 	// if the request is triggered cool down by the runaway checker, we need to adjust the concurrency, let the sql run slowly.
 	if req.RunawayChecker != nil && req.RunawayChecker.CheckAction() == rmpb.RunawayAction_CoolDown {
 		it.concurrency = 1
@@ -835,15 +841,16 @@ func (worker *copIteratorWorker) run(ctx context.Context) {
 // open starts workers and sender goroutines.
 func (it *copIterator) open(ctx context.Context, enabledRateLimitAction, enableCollectExecutionInfo bool) {
 	taskCh := make(chan *copTask, 1)
-	smallTaskCh := make(chan *copTask, 1)
 	it.unconsumedStats = &unconsumedCopRuntimeStats{}
 	it.wg.Add(it.concurrency + it.smallTaskConcurrency)
+	var smallTaskCh chan *copTask
+	if it.smallTaskConcurrency > 0 {
+		smallTaskCh = make(chan *copTask, 1)
+	}
 	// Start it.concurrency number of workers to handle cop requests.
 	for i := 0; i < it.concurrency+it.smallTaskConcurrency; i++ {
-		var ch chan *copTask
-		if i < it.concurrency {
-			ch = taskCh
-		} else {
+		ch := taskCh
+		if i >= it.concurrency && smallTaskCh != nil {
 			ch = smallTaskCh
 		}
 		worker := &copIteratorWorker{
@@ -897,7 +904,7 @@ func (sender *copIteratorTaskSender) run(connID uint64, checker resourcegroup.Ru
 			break
 		}
 		var sendTo chan<- *copTask
-		if isSmallTask(t) {
+		if isSmallTask(t) && sender.smallTaskCh != nil {
 			sendTo = sender.smallTaskCh
 		} else {
 			sendTo = sender.taskCh
@@ -911,7 +918,9 @@ func (sender *copIteratorTaskSender) run(connID uint64, checker resourcegroup.Ru
 		}
 	}
 	close(sender.taskCh)
-	close(sender.smallTaskCh)
+	if sender.smallTaskCh != nil {
+		close(sender.smallTaskCh)
+	}
 
 	// Wait for worker goroutines to exit.
 	sender.wg.Wait()