Thanks, this is helpful and why I came to the comments. Another question I had was what happens to red? You helped me answer that -- unlike echo green, the output of echo red is still connected to the pipe. The right-hand side of that pipe does nothing with it, so it disappears.

Also regarding one of your examples: maybe I'm misunderstanding, and anyway this wouldn't change your overall point, but should it maybe read like this instead: bash -c '(echo green 1>&2) | echo blue' 1>stdout 2>stderr

since stdin is normally associated with file descriptor 0