Regarding special cases on the reading side, I think there should be an easy way to distinguish them. The existing RawIOBase way is probably as good as any, unless you want to take the chance to invent a better API:

* EOF (pipe closed, no more data ever) should be indicated by returning b""
* Empty pipe (still open, future data possible) should be indicated by returning None

Beware that BlockingIOError is normally not raised by Python’s standard library, despite the BufferedIOBase documentation, and I think it should say that way (the implementation, that is). See Issue 13322.

Regarding handling a broken pipe condition, it would be nice to have a way of signalling that to the caller, whether via an exception or other means. For example if the subprocess is a video player which gets closed early by the end user, it would be good to know to stop wasting time and bandwidth generating and piping video the the player.