diff --git a/Lib/test/test_cmd_line.py b/Lib/test/test_cmd_line.py
index 56a8e39..8167e78 100644
--- a/Lib/test/test_cmd_line.py
+++ b/Lib/test/test_cmd_line.py
@@ -272,6 +272,25 @@
         self.assertRegex(err.decode('ascii', 'ignore'), 'SyntaxError')
         self.assertEqual(b'', out)
 
+    def test_stdout_flush_at_shutdown(self):
+        # Issue #5319: if stdout.flush() fails at shutdown, an error should
+        # be printed out.
+        code = """if 1:
+            import os, sys
+            sys.stdout.write('x')
+            os.close(sys.stdout.fileno())"""
+        rc, out, err = assert_python_ok('-c', code)
+        self.assertEqual(b'', out)
+        self.assertRegex(err.decode('ascii', 'ignore'),
+                         'Exception IOError: .* ignored')
+
+    def test_closed_stdout(self):
+        # Issue #13444: if stdout has been explicitly closed, we should
+        # not attempt to flush it at shutdown.
+        code = "import sys; sys.stdout.close()"
+        rc, out, err = assert_python_ok('-c', code)
+        self.assertEqual(b'', err)
+
 
 def test_main():
     test.support.run_unittest(CmdLineTest)
diff --git a/Misc/NEWS b/Misc/NEWS
index fba2c3d..eaadaaf 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -83,6 +83,9 @@
 Library
 -------
 
+- Issue #13444: When stdout has been closed explicitly, we should not attempt
+  to flush it at shutdown and print an error.
+
 - Issue #12856: Ensure child processes do not inherit the parent's random
   seed for filename generation in the tempfile module.  Patch by Brian
   Harring.
diff --git a/Python/pythonrun.c b/Python/pythonrun.c
index bea7fe1..fe92d30 100644
--- a/Python/pythonrun.c
+++ b/Python/pythonrun.c
@@ -332,6 +332,22 @@
 
 /* Flush stdout and stderr */
 
+static int
+file_is_closed(PyObject *fobj)
+{
+    int r;
+    PyObject *tmp = PyObject_GetAttrString(fobj, "closed");
+    if (tmp == NULL) {
+        PyErr_Clear();
+        return 0;
+    }
+    r = PyObject_IsTrue(tmp);
+    Py_DECREF(tmp);
+    if (r < 0)
+        PyErr_Clear();
+    return r > 0;
+}
+
 static void
 flush_std_files(void)
 {
@@ -339,7 +355,7 @@
     PyObject *ferr = PySys_GetObject("stderr");
     PyObject *tmp;
 
-    if (fout != NULL && fout != Py_None) {
+    if (fout != NULL && fout != Py_None && !file_is_closed(fout)) {
         tmp = PyObject_CallMethod(fout, "flush", "");
         if (tmp == NULL)
             PyErr_WriteUnraisable(fout);
@@ -347,7 +363,7 @@
             Py_DECREF(tmp);
     }
 
-    if (ferr != NULL && ferr != Py_None) {
+    if (ferr != NULL && ferr != Py_None && !file_is_closed(ferr)) {
         tmp = PyObject_CallMethod(ferr, "flush", "");
         if (tmp == NULL)
             PyErr_Clear();