When address group is missing final ';', 'value' will be an empty string. I suggest the following patch

$ diff -u _save_header_value_parser.py _header_value_parser.py
--- _save_header_value_parser.py        2018-03-14 01:07:54.000000000 +0100
+++ _header_value_parser.py     2018-05-13 02:17:13.830053600 +0200
@@ -1876,7 +1876,7 @@
     if not value:
         group.defects.append(errors.InvalidHeaderDefect(
             "end of header in group"))
-    if value[0] != ';':
+    elif value[0] != ';':
         raise errors.HeaderParseError(
             "expected ';' at end of group but found {}".format(value))
     group.append(ValueTerminal(';', 'group-terminator'))

The fix is mostly likely correct, so we need a PR for this that includes tests.

Unsure how to issue a "PR" (Problem Report?) with a test case.

Here is my best effort:

Create a file "email.eml" in the current directory, as attached.
(The contents were lifted from RFC2822 section A.1.3, but I deleted the ";" at the end of the "To" header. The file has CRLF line endings.)

Then run the following test program (It appears that I can only attach one file to this ).

$ cat test-bug.py
from email.policy import default
import email

with open('email.eml', 'rb') as f:
    msg = email.message_from_binary_file(f, policy=default)
    toheader = msg['To']
    for addr in toheader.addresses:
        print(addr)

#----------------------------------------------------
# Output without the fix:

$ python3.6.5 test-bug.py
Traceback (most recent call last):
  File "test-bug.py", line 6, in <module>
    toheader = msg['To']
  File "C:\Program Files\Python36\lib\email\message.py", line 391, in __getitem__
    return self.get(name)
  File "C:\Program Files\Python36\lib\email\message.py", line 471, in get
    return self.policy.header_fetch_parse(k, v)
  File "C:\Program Files\Python36\lib\email\policy.py", line 162, in header_fetch_parse
    return self.header_factory(name, value)
  File "C:\Program Files\Python36\lib\email\headerregistry.py", line 589, in __call__
    return self[name](name, value)
  File "C:\Program Files\Python36\lib\email\headerregistry.py", line 197, in __new__
    cls.parse(value, kwds)
  File "C:\Program Files\Python36\lib\email\headerregistry.py", line 340, in parse
    kwds['parse_tree'] = address_list = cls.value_parser(value)
  File "C:\Program Files\Python36\lib\email\headerregistry.py", line 331, in value_parser
    address_list, value = parser.get_address_list(value)
  File "C:\Program Files\Python36\lib\email\_header_value_parser.py", line 1931, in get_address_list
    token, value = get_address(value)
  File "C:\Program Files\Python36\lib\email\_header_value_parser.py", line 1908, in get_address
    token, value = get_group(value)
  File "C:\Program Files\Python36\lib\email\_header_value_parser.py", line 1879, in get_group
    if value[0] != ';':
IndexError: string index out of range

#-----------------------------------------------------
# Output with the fix:

$ test-bug.py
Chris Jones <c@a.test>
joe@where.test
John <jdoe@one.test>

@Cacadril

Please send a pull request(PR) through CPython GitHub(https://github.com/python/cpython)

It will be a great experience :)

@r.david.murray

Please take a look PR 7484 :)

@r.david.murray
Can I get a review for PR 7484?

New changeset 8fe9eed937cb69b5e26ac6e36a90b5360eb11277 by Steve Dower (Dong-hee Na) in branch 'master':
bpo-33476: Fix _header_value_parser when address group is missing final ';' (GH-7484)
https://github.com/python/cpython/commit/8fe9eed937cb69b5e26ac6e36a90b5360eb11277

New changeset 2be0124b820729eacc1288950b824e336bd3a4a6 by Miss Islington (bot) in branch '3.7':
bpo-33476: Fix _header_value_parser when address group is missing final ';' (GH-7484)
https://github.com/python/cpython/commit/2be0124b820729eacc1288950b824e336bd3a4a6

New changeset f17e001746e0f697e9bd49ac3748f2543b0a0d47 by Miss Islington (bot) in branch '3.6':
bpo-33476: Fix _header_value_parser when address group is missing final ';' (GH-7484)
https://github.com/python/cpython/commit/f17e001746e0f697e9bd49ac3748f2543b0a0d47