It looks like a bug in the subprocess module e.g., if child process does:

  sys.stdout.write(sys.stdin.readline())
  sys.stdout.flush()

and the parent:

   p.stdin.write(line) #NOTE: no flush
   line = p.stdout.readline()

then a deadlock may happen with bufsize=1 (because it is equivalent to bufsize=-1 in the current code)

Surprisingly, it works if universal_newlines=True but only for C implementation of io i.e., if C extension is disabled:

  import io, _pyio 
  io.TextIOWrapper = _pyio.TextIOWrapper

then it blocks forever even if universal_newlines=True with bufsize=1 that is clearly wrong (<-- bug) e.g., `test_universal_newlines` deadlocks with _pyio.TextIOWrapper

C implementation works because it sets `needflush` flag even if only `write_through` is provided [1]:

    if (self->write_through)
        needflush = 1;
    else if (self->line_buffering &&
        (haslf ||
         PyUnicode_FindChar(text, '\r', 0, PyUnicode_GET_LENGTH(text), 1) != -1))
        needflush = 1;

[1]: http://hg.python.org/cpython/file/0b2e199ad088/Modules/_io/textio.c#l1333

Python io implementation doesn't flush with only `write_through` flag.

It doesn't deadlock if bufsize=0 whether universal_newlines=True or not.

Note: Python 2.7 doesn't deadlock with bufsize=0 and bufsize=1 in this case as expected.

What is not clear is whether it should work with universal_newline=False and bufsize=1: both current docs and Python 2.7 behaviour say that there should not be a deadlock.

I've updated the docs to mention that bufsize=1 works only with 
universal_newlines=True and added corresponding tests. I've also updated the subprocess' code to pass line_buffering explicitly.

Patch is uploaded.