I actually could not replicate your result*, in my case your loop runs through and it'd fail on the assert as p has not finished yet and has no returncode (or rather its value is still None at that time). Inserting p.wait() after the loop and before the assert would force we only check for result after p has terminated.
Now for the exception you're seeing, it most likely indicates the pipe you're trying to perform flush() on is closed. Most likely due to the process having already terminated. Perhaps in your case at that point it already has a (non-zero) returncode too which could further help understand the problem?**
* On my system /bin/sh used by subprocess.Popen() with shell=True is actually bash. Running ["/bin/dash", "-c", "read"] which presumably happens to be shell called for /bin/sh on your system, I got broken pipe as well.
** Running dash like this seems to fail with:
/bin/dash: 1: read: arg count
And return 2.
Which sort of makes it more of a dash question: why calling /bin/dash -c "read" (from python) fails. It appears that dash read (unlike its bash counterpart) always expect at least one variable name to read into as an argument (replace read with read foo).
I guess this python question just became a lesson about assumptions and shell scripts portability. :)