diff --git a/Lib/test/test_textwrap.py b/Lib/test/test_textwrap.py
index aca1f427656bb5..ea8b3bfcc65b08 100644
--- a/Lib/test/test_textwrap.py
+++ b/Lib/test/test_textwrap.py
@@ -615,6 +615,18 @@ def test_break_long(self):
                          'word,',
                          'anyways?'])
 
+    def test_indent_wider_than_width(self):
+        # These used to loop forever or to add an extra last line when the
+        # indent was not narrower than the width.
+        self.check_wrap(' x', 1, ['  x'], initial_indent='  ')
+        self.check_wrap(' ', 5, [], initial_indent='      ')
+        self.check_wrap('abc', 2, ['ab', '   c'],
+                        subsequent_indent='   ', drop_whitespace=False)
+        self.check_wrap('x', 1, ['  x'],
+                        initial_indent='  ', drop_whitespace=False)
+        self.check_wrap('abcdef', 3, ['abc', '   d', '   e', '   f'],
+                        subsequent_indent='   ', drop_whitespace=False)
+
     def test_nobreak_long(self):
         # Test with break_long_words disabled
         self.wrapper.break_long_words = 0
diff --git a/Lib/textwrap.py b/Lib/textwrap.py
index 2f213e34c2c329..b04b6301914ae0 100644
--- a/Lib/textwrap.py
+++ b/Lib/textwrap.py
@@ -221,7 +221,12 @@ def _handle_long_word(self, reversed_chunks, cur_line, cur_len, width):
                 if hyphen > 0 and any(c != '-' for c in chunk[:hyphen]):
                     end = hyphen + 1
             cur_line.append(chunk[:end])
-            reversed_chunks[-1] = chunk[end:]
+            if end < len(chunk):
+                reversed_chunks[-1] = chunk[end:]
+            else:
+                # The whole chunk fit, which happens only when the indent is
+                # not narrower than the width.  Don't leave an empty chunk.
+                reversed_chunks.pop()
 
         # Otherwise, we have to preserve the long word intact.  Only add
         # it to the current line if there's nothing already there --
diff --git a/Misc/NEWS.d/next/Library/2026-10-07-12-21-15.gh-issue-158979.TkrgLs.rst b/Misc/NEWS.d/next/Library/2026-10-07-12-21-15.gh-issue-158979.TkrgLs.rst
new file mode 100644
index 00000000000000..9d82d494b42033
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2026-10-07-12-21-15.gh-issue-158979.TkrgLs.rst
@@ -0,0 +1,4 @@
+Fix an infinite loop in :func:`textwrap.wrap` and :func:`textwrap.fill` when
+the indent is wider than *width* and the text starts with whitespace, or
+*drop_whitespace* is false. They also no longer add an empty or indent-only
+last line in some cases where the indent is not narrower than *width*.