GH-85760: Fix race in calling process_exited callback too early (GH-97009)

(cherry picked from commit 282edd7b2a74c4dfe1bfe3c5b1d30f9c21d554d6)

Co-authored-by: Kumar Aditya <59607654+kumaraditya303@users.noreply.github.com>
diff --git a/Lib/asyncio/unix_events.py b/Lib/asyncio/unix_events.py
index c88b818..39b5e83 100644
--- a/Lib/asyncio/unix_events.py
+++ b/Lib/asyncio/unix_events.py
@@ -223,7 +223,8 @@
         return transp
 
     def _child_watcher_callback(self, pid, returncode, transp):
-        self.call_soon_threadsafe(transp._process_exited, returncode)
+        # Skip one iteration for callbacks to be executed
+        self.call_soon_threadsafe(self.call_soon, transp._process_exited, returncode)
 
     async def create_unix_connection(
             self, protocol_factory, path=None, *,
diff --git a/Misc/NEWS.d/next/Library/2022-09-22-11-50-29.gh-issue-85760.DETTPd.rst b/Misc/NEWS.d/next/Library/2022-09-22-11-50-29.gh-issue-85760.DETTPd.rst
new file mode 100644
index 0000000..af8ae20
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2022-09-22-11-50-29.gh-issue-85760.DETTPd.rst
@@ -0,0 +1 @@
+Fix race condition in :mod:`asyncio` where :meth:`~asyncio.SubprocessProtocol.process_exited` called before the :meth:`~asyncio.SubprocessProtocol.pipe_data_received` leading to inconsistent output. Patch by Kumar Aditya.