diff --git a/AUTHORS b/AUTHORS
index 6d860575f37..be1e7863860 100644
--- a/AUTHORS
+++ b/AUTHORS
@@ -337,6 +337,7 @@ Serhii Mozghovyi
 Seth Junot
 Shantanu Jain
 Shubham Adep
+Simon Blanchard
 Simon Gomizelj
 Simon Holesch
 Simon Kerr
diff --git a/changelog/11439.bugfix.rst b/changelog/11439.bugfix.rst
new file mode 100644
index 00000000000..b5104b1bcab
--- /dev/null
+++ b/changelog/11439.bugfix.rst
@@ -0,0 +1 @@
+Handle an edge case where :data:`sys.stderr` might already be closed when :ref:`faulthandler` is tearing down.
diff --git a/src/_pytest/faulthandler.py b/src/_pytest/faulthandler.py
index af879aa44cf..36040bffffc 100644
--- a/src/_pytest/faulthandler.py
+++ b/src/_pytest/faulthandler.py
@@ -1,4 +1,3 @@
-import io
 import os
 import sys
 from typing import Generator
@@ -51,7 +50,7 @@ def get_stderr_fileno() -> int:
         if fileno == -1:
             raise AttributeError()
         return fileno
-    except (AttributeError, io.UnsupportedOperation):
+    except (AttributeError, ValueError):
         # pytest-xdist monkeypatches sys.stderr with an object that is not an actual file.
         # https://docs.python.org/3/library/faulthandler.html#issue-with-file-descriptors
         # This is potentially dangerous, but the best we can do.