I haven't know MySQL allows such a broken date...
But Python's date doesn't allow such date.
What PyMySQL can do for everyone, not only for you?

Python 3.5.2 (default, Sep 28 2016, 18:08:09)
[GCC 4.2.1 Compatible Apple LLVM 8.0.0 (clang-800.0.38)] on darwin
Type "help", "copyright", "credits" or "license" for more information.
>>> import datetime
>>> datetime.date(2016, 0, 0)
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
ValueError: month must be in 1..12

Maybe, as a simple solution for now, just return it as a string in that case?

Maybe there are also other datetime-like libraries which support a data structure which allows this, but I don't know any and this would add another dependency so that might not be an option.

Hm, But doesn't it break compatibility?

Some existing code (ORMs) may not expect string is returned for date column.
But all existing code should support it, since there are NULLABLE column...

Additionally, is the date is supported by MySQL when sql_mode is strict?

I think you shouldn't use date column type, string or integer is better.

I agree that this might be cleaner, however, I have an existing DB without NO_ZERO_IN_DATE and I still would like to use pymysql (and maybe even better peewee on top).

I think peewee also supports strings, as it could get strings from some other DB backends.

peewee is not only user of PyMySQL.
PyMySQL supports customizing converters for such a special edge cases.

from pymysql.constants import FIELD_TYPE
from pymysql.converters import conversions as conv, 
conv = conv.copy()

del conv[FIELD_TYPE.DATE]
del conv[FIELD_TYPE.DATETIME]
del conv[FIELD_TYPE.TIME]

conn = pymysql.connect(..., conv=conv)

FWIW I have a MySQL database that I've been using for years, with no special configuration, which has always accepted dates like 2016-03-00 and 2016-00-00 and have just discovered this issue too.

It'd be good to have the stuff about customising the converters, and why you might want to do so, in the documentation.

I'm not good at English. Writing English is 1000x harder than writing Python.
Contribution is welcome.

I still open this because I feel "fallback to string" is acceptable idea.

MySQL 5.7; db with NO_ZERO_IN_DATE eliminated from default. Python 3.6 using Alchemy will find "1920-00-00" when specifically requested as "SELECT history-date FROM table;" but "SELECT * FROM table;" brings back a null. Using variable dict.
Any solutions?