$ ./python.exe nopickle.py
TypeError: __init__() missing 1 required positional argument: 'num'

The issue is that the arguments passed to Exception.__init__ (via `super()`) are collected into `args` and then serialized by pickle e.g.

>>> PickleBreaker(5).args
()
>>> PickleBreaker(5).__reduce_ex__(3)
(<class '__main__.PoolBreaker'>, (), {'num': 5})
>>> # The 1st index is the `args` tuple

Then, during load, the `args` tuple is used to initialize the Exception i.e. PickleBreaker(), which results in the `TypeError`

See https://github.com/python/cpython/blob/master/Modules/_pickle.c#L6769

possibly related to https://bugs.python.org/issue32696 and https://bugs.python.org/issue1692335.

It seems to that this problem is affecting __new__ methods independent of exceptions:

>>> class NewBreaker:
...     def __new__(cls, arg):
...             return super().__new__(cls)
...
>>> nb = NewBreaker(42)
>>> import pickle
>>> dumped = pickle.dumps(nb)
>>> pickle.loads(dumped)
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
TypeError: __new__() missing 1 required positional argument: 'arg'

This is the same as issue32696.

I'm turning this into a documentation issue.