@@ -1023,6 +1023,10 @@ def _readfrom(cls, fileobj=None, data=None, mode=None,
         # If we're trying to read only and no header units were found,
         # raise an exception
         if not read_one and mode in ('readonly', 'denywrite'):
+            # Close the file if necessary (issue #6168)
+            if hdulist._file.close_on_error:
+                hdulist._file.close()
+
             raise IOError('Empty or corrupt FITS file')
 
         if not lazy_load_hdus:
 
@@ -918,7 +918,8 @@ def test_proper_error_raised_on_non_fits_file_with_unicode(self):
     # Avoid a spurious pyflakes warning about an unused import
     # of six by adding a reason string
     @pytest.mark.skipif(six.PY2, reason='six.PY2')
-    def test_no_resource_warning_raised_on_non_fits_file(self):
+    @pytest.mark.parametrize(('ignore', ), [(False, ), (True, )])
+    def test_no_resource_warning_raised_on_non_fits_file(self, ignore):
         """
         Regression test for https://github.com/astropy/astropy/issues/6168
 
@@ -933,7 +934,7 @@ def test_no_resource_warning_raised_on_non_fits_file(self):
         # This should raise an IOError because there is no end card.
         with catch_warnings(ResourceWarning) as ws:
             with pytest.raises(IOError):
-                fits.open(filename)
+                fits.open(filename, ignore_missing_end=ignore)
 
         assert len(ws) == 0