diff --git a/lib/ansible/plugins/strategy/linear.py b/lib/ansible/plugins/strategy/linear.py
index 29721983cc7..6c27a13787a 100644
--- a/lib/ansible/plugins/strategy/linear.py
+++ b/lib/ansible/plugins/strategy/linear.py
@@ -265,6 +265,8 @@ class StrategyModule(StrategyBase):
                         results.extend(self._execute_meta(task, play_context, iterator, host))
                         if task.args.get('_raw_params', None) not in ('noop', 'reset_connection'):
                             run_once = True
+                        if (task.any_errors_fatal or run_once) and not task.ignore_errors:
+                            any_errors_fatal = True
                     else:
                         # handle step if needed, skip meta actions as they are used internally
                         if self._step and choose_step:
@@ -402,7 +404,9 @@ class StrategyModule(StrategyBase):
                 failed_hosts = []
                 unreachable_hosts = []
                 for res in results:
-                    if res.is_failed() and iterator.is_failed(res._host):
+                    # execute_meta() does not set 'failed' in the TaskResult
+                    # so we skip checking it with the meta tasks and look just at the iterator
+                    if (res.is_failed() or res._task.action == 'meta') and iterator.is_failed(res._host):
                         failed_hosts.append(res._host.name)
                     elif res.is_unreachable():
                         unreachable_hosts.append(res._host.name)
diff --git a/test/integration/targets/handlers/runme.sh b/test/integration/targets/handlers/runme.sh
index 726d8094c7e..fdeb8682750 100755
--- a/test/integration/targets/handlers/runme.sh
+++ b/test/integration/targets/handlers/runme.sh
@@ -57,3 +57,9 @@ grep -q "ERROR! The requested handler 'notify_inexistent_handler' was not found
 # Notify inexistent handlers without errors when ANSIBLE_ERROR_ON_MISSING_HANDLER=false
 ANSIBLE_ERROR_ON_MISSING_HANDLER=false ansible-playbook test_handlers_inexistent_notify.yml -i inventory.handlers -v "$@"
 
+# https://github.com/ansible/ansible/issues/36649
+output_dir=/tmp
+set +e
+result="$(ansible-playbook test_handlers_any_errors_fatal.yml -e output_dir=$output_dir -i inventory.handlers -v "$@" 2>&1)"
+set -e
+[ ! -f $output_dir/should_not_exist_B ] || (rm -f $output_dir/should_not_exist_B && exit 1)
diff --git a/test/integration/targets/handlers/test_handlers_any_errors_fatal.yml b/test/integration/targets/handlers/test_handlers_any_errors_fatal.yml
new file mode 100644
index 00000000000..9029443a6fe
--- /dev/null
+++ b/test/integration/targets/handlers/test_handlers_any_errors_fatal.yml
@@ -0,0 +1,25 @@
+- hosts:
+    - A
+    - B
+  gather_facts: no
+  any_errors_fatal: yes
+  connection: local
+  vars:
+    output_dir: /tmp
+  tasks:
+    - name: Task one
+      debug:
+        msg: 'task 1'
+      changed_when: yes
+      notify: EXPECTED FAILURE failed_handler
+
+    - meta: flush_handlers
+
+    - name: This task should never happen
+      file:
+        path: "{{ output_dir }}/should_not_exist_{{ inventory_hostname }}"
+        state: touch
+  handlers:
+    - name: EXPECTED FAILURE failed_handler
+      fail:
+      when: 'inventory_hostname == "A"'