diff --git a/CHANGES.rst b/CHANGES.rst
index 493cf2d88..cfc786ad8 100644
--- a/CHANGES.rst
+++ b/CHANGES.rst
@@ -15,6 +15,8 @@ Unreleased
     empty. :issue:`3019` :pr:`3021`
 -   When ``Sentinel.UNSET`` is found during parsing, it will skip calls to
     ``type_cast_value``. :issue:`3069` :pr:`3090`
+-   Fix regression related to ``click.testing.StreamMixer`` finalization in ``CliRunner``
+    that introduced a race condition. :issue:`3110` :pr:`3140`
 
 Version 8.3.0
 --------------
diff --git a/src/click/testing.py b/src/click/testing.py
index f6f60b809..e734ddd08 100644
--- a/src/click/testing.py
+++ b/src/click/testing.py
@@ -72,16 +72,20 @@ class BytesIOCopy(io.BytesIO):
     .. versionadded:: 8.2
     """
 
+    copy_to: io.BytesIO
+
     def __init__(self, copy_to: io.BytesIO) -> None:
         super().__init__()
         self.copy_to = copy_to
 
     def flush(self) -> None:
+        if not self.copy_to.closed:
+            self.copy_to.flush()
         super().flush()
-        self.copy_to.flush()
 
     def write(self, b: ReadableBuffer) -> int:
-        self.copy_to.write(b)
+        if not self.copy_to.closed:
+            self.copy_to.write(b)
         return super().write(b)
 
 
@@ -100,15 +104,15 @@ def __init__(self) -> None:
 
     def __del__(self) -> None:
         """
-        Guarantee that embedded file-like objects are closed in a
+        Guarantee that embedded file-like objects are deleted in a
         predictable order, protecting against races between
-        self.output being closed and other streams being flushed on close
+        self.output being deleted and other streams being flushed on deletion.
 
         .. versionadded:: 8.2.2
         """
-        self.stderr.close()
-        self.stdout.close()
-        self.output.close()
+        del self.stdout
+        del self.stderr
+        del self.output
 
 
 class _NamedTextIOWrapper(io.TextIOWrapper):