diff --git a/Lib/test/test_textwrap.py b/Lib/test/test_textwrap.py
index aca1f427656bb5..99fce6f241e007 100644
--- a/Lib/test/test_textwrap.py
+++ b/Lib/test/test_textwrap.py
@@ -760,6 +760,14 @@ def test_subsequent_indent(self):
                       initial_indent="  * ", subsequent_indent="    ")
         self.check(result, expect)
 
+    def test_indent_longer_than_width(self):
+        # gh-160558: wrap() looped forever when an indent was longer than
+        # width.
+        self.check_wrap(" ", 3, [], initial_indent="----")
+        self.check_wrap(" a", 3, ["----a"], initial_indent="----")
+        self.check_wrap("aaaa", 3, ["aaa", "----a", "----"],
+                        subsequent_indent="----", drop_whitespace=False)
+
 
 # Despite the similar names, DedentTestCase is *not* the inverse
 # of IndentTestCase!
diff --git a/Lib/textwrap.py b/Lib/textwrap.py
index 2f213e34c2c329..ca87df5f46cb56 100644
--- a/Lib/textwrap.py
+++ b/Lib/textwrap.py
@@ -288,7 +288,7 @@ def _wrap_chunks(self, chunks):
                 l = len(chunks[-1])
 
                 # Can at least squeeze this chunk onto the current line.
-                if cur_len + l <= width:
+                if cur_len + l <= width or not l:
                     cur_line.append(chunks.pop())
                     cur_len += l
 
diff --git a/Misc/NEWS.d/next/Library/2026-10-24-00-53-48.gh-issue-160558.XyEOEz.rst b/Misc/NEWS.d/next/Library/2026-10-24-00-53-48.gh-issue-160558.XyEOEz.rst
new file mode 100644
index 00000000000000..0c0e2c6632df7a
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2026-10-24-00-53-48.gh-issue-160558.XyEOEz.rst
@@ -0,0 +1,2 @@
+Fix :func:`textwrap.wrap` and :func:`textwrap.fill` hanging in some cases
+when *initial_indent* or *subsequent_indent* is longer than *width*.