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'