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Keeping the sys.stdin reference alive and then reassigning sys.stdin prevents exit() and quit() from actually closing IDLE since site.py's code closes sys.stdin which then does not trigger PyShell's close() method. I updated Terry's patch to explicitly call the close method when SystemExit gets raised.
IDLE's subprocess clears atexit handlers before shutdown so they never get called. See exit() from Lib/idlelib/run.py.
The debugger can not handle stepping through a "raise SystemExit" from the shell, even long before any sys.std* patches got applied. That's a separate issue that should be opened. I mention that so that if anyone manually tests with the debugger that this behavior is "expected".