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easy enough to reproduce...
$ ./python.exe -c 'import os, subprocess as s; os.close(0); os.close(1); s.Popen(["/bin/true"])'
Traceback (most recent call last):
 File "<string>", line 1, in <module>
 File "/Users/gps/python/hg/default/Lib/subprocess.py", line 818, in __init__
 restore_signals, start_new_session)
 File "/Users/gps/python/hg/default/Lib/subprocess.py", line 1363, in _execute_child
 restore_signals, start_new_session, preexec_fn)
ValueError: errpipe_write must be >= 3
Examining the code, it looks like that restriction is to prevent the dup2's for any passed in stdin, stdout or stderr pipes from overwriting errpipe_write in Modules/_posixsubprocess.c's child_exec() function.
First guess at a fix: child_exec() needs to detect this situation and dup(errpipe_write) until it gets a fd not in the 0..2 range before the dup2(...) calls that could otherwise blindly clobber it. This could possibly be done by the parent process's _create_pipe() in Lib/subprocess.py when allocating the errpipe_read and errpipe_write fds.
Suggested Workaround: for now for any code running into this (Python daemons launching subprocesses?) - Call os.pipe() twice at the start of your program to burn 4 fds. That'll guarantee 0, 1 and 2 will not be used for this pipe.