>>> import pandas as pd
>>> import numpy as np

>>> ix1 = pd.MultiIndex.from_arrays([[np.nan, 81, 81, 82, 82], [np.nan, np.nan, np.nan, np.nan, np.nan], pd.to_datetime([np.nan, '2018-06-01', '2018-07-01', '2018-07-01', '2018-08-01'])], names=['foo', 'bar', 'date'])
>>> ix1
MultiIndex([( nan, nan,        'NaT'),
            (81.0, nan, '2018-06-01'),
            (81.0, nan, '2018-07-01'),
            (82.0, nan, '2018-07-01'),
            (82.0, nan, '2018-08-01')],
           names=['foo', 'bar', 'date'])
>>>
>>> s1 = pd.Series([np.nan, 25.058969, 22.519751, 20.847981, 21.625236], index=ix1)
>>> s1
foo  bar  date
NaN  NaN  NaT                 NaN
81   NaN  2018-06-01    25.058969
          2018-07-01    22.519751
82   NaN  2018-07-01    20.847981
          2018-08-01    21.625236
dtype: float64
>>>
>>> ix2 = pd.Index([81, 82, 83, 84, 85, 86, 87], name='foo')
>>> ix2
Index([81, 82, 83, 84, 85, 86, 87], dtype='int64', name='foo')
>>>
>>> s2 = pd.Series([28.2800, 25.2500, 22.2200, 16.7660, 14.0087, 14.9480, 29.2900], ix2)
>>>
>>> s2
foo
81    28.2800
82    25.2500
83    22.2200
84    16.7660
85    14.0087
86    14.9480
87    29.2900
dtype: float64
>>>
>>>
>>> s1 - s2
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File ".venv/lib64/python3.11/site-packages/pandas/core/ops/common.py", line 76, in new_method
    return method(self, other)
           ^^^^^^^^^^^^^^^^^^^
  File ".venv/lib64/python3.11/site-packages/pandas/core/arraylike.py", line 194, in __sub__
    return self._arith_method(other, operator.sub)
           ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File ".venv/lib64/python3.11/site-packages/pandas/core/series.py", line 5814, in _arith_method
    self, other = self._align_for_op(other)
                  ^^^^^^^^^^^^^^^^^^^^^^^^^
  File ".venv/lib64/python3.11/site-packages/pandas/core/series.py", line 5844, in _align_for_op
    left, right = left.align(right, copy=False)
                  ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File ".venv/lib64/python3.11/site-packages/pandas/core/generic.py", line 10091, in align
    left, _right, join_index = self._align_series(
                               ^^^^^^^^^^^^^^^^^^^
  File ".venv/lib64/python3.11/site-packages/pandas/core/generic.py", line 10213, in _align_series
    left = self._reindex_indexer(join_index, lidx, copy)
           ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File ".venv/lib64/python3.11/site-packages/pandas/core/series.py", line 4782, in _reindex_indexer
    return self._constructor(new_values, index=new_index, copy=False)
           ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File ".venv/lib64/python3.11/site-packages/pandas/core/series.py", line 503, in __init__
    com.require_length_match(data, index)
  File ".venv/lib64/python3.11/site-packages/pandas/core/common.py", line 561, in require_length_match
    raise ValueError(
ValueError: Length of values (5) does not match length of index (4)

>>> s1.iloc[1:] - s2  # proactively removing the all-nan index row allows the operation to succeed without error
foo  bar  date      
81   NaN  2018-06-01   -3.221031
          2018-07-01   -5.760249
82   NaN  2018-07-01   -4.402019
          2018-08-01   -3.624764
dtype: float64

class Series(...):
    ...
    def _align_series(...):
        ...
        if not axis:
            # equal
            if self.index.equals(other.index):
                join_index, lidx, ridx = None, None, None
            else:
                join_index, lidx, ridx = self.index.join(
                    other.index, how=join, level=level, return_indexers=True
                )

                ## At this point, `join_index` is invalid as it contains different length codes:
                ## join_index.code ==  FrozenList([[0, 0, 1, 1], [-1, -1, -1, -1, -1], [-1, 0, 1, 1, 2]])
                ## which returns (4 items in level index 0)
                ##   join_index.get_level_values(0) ==           Index([81.0, 81.0, 82.0, 82.0], dtype='float64', name='foo')
                ## while (5 items in level index 1 and 2)
                ##   join_index.get_level_values(1) ==           Index([nan,   nan,  nan,  nan, nan], dtype='float64', name='demand_index')
                ##   join_index.get_level_values(2) == DatetimeIndex(['NaT', '2018-06-01', '2018-07-01', '2018-07-01', '2018-08-01'], dtype='datetime64[ns]', name='blend_date', freq=None)
                ##

            if is_series:
                ## The invalid `join_index` is picked up by `._reindex_indexer(...)` as `len(join_index)` == 4 and `len(new_values) == 5` which causes the `ValueError`
                left = self._reindex_indexer(join_index, lidx, copy)
        ...



    def _reindex_indexer(...):
        ...
        new_values = algorithms.take_nd(
            self._values, indexer, allow_fill=True, fill_value=None
        )
        return self._constructor(new_values, index=new_index, copy=False)  ## <- raises the ValueError

class Index(...):
     def _join_level(...):
        ...
        else:
            left_lev_indexer = ensure_platform_int(left_lev_indexer)
            rev_indexer = lib.get_reverse_indexer(left_lev_indexer, len(old_level))
            old_codes = left.codes[level]

            ## This will ignore missing values (nan) without ever inserting
            ## those values back into the index, ultimately leading to
            ## different length codes
            taker = old_codes[old_codes != -1]
            new_lev_codes = rev_indexer.take(taker)

            new_codes = list(left.codes)
            new_codes[level] = new_lev_codes

            new_levels = list(left.levels)
            new_levels[level] = new_level

            if keep_order:  # just drop missing values. o.w. keep order
                left_indexer = np.arange(len(left), dtype=np.intp)
                left_indexer = cast(np.ndarray, left_indexer)
                mask = new_lev_codes != -1
                if not mask.all():
                    new_codes = [lab[mask] for lab in new_codes]
                    left_indexer = left_indexer[mask]
            ...
            join_index = MultiIndex(
                levels=new_levels,
                codes=new_codes,
                names=left.names,
                verify_integrity=False,
            )

class MultiIndex(...):
    def __new__(...):
        ...
        # result._set_codes(codes, copy=copy, validate=False)
        result._set_codes(codes, copy=copy, validate=False, verify_integrity=True)
        ...

>>> s1
foo  bar  date
NaN  NaN  NaT                 NaN
81   NaN  2018-06-01    25.058969
          2018-07-01    22.519751
82   NaN  2018-07-01    20.847981
          2018-08-01    21.625236
dtype: float64
>>> s2
foo
81    28.2800
82    25.2500
83    22.2200
84    16.7660
85    14.0087
86    14.9480
87    29.2900
dtype: float64
>>> s1 - s2
foo  bar  date      
NaN  NaN  NaT                NaN
81   NaN  2018-06-01   -3.221031
          2018-07-01   -5.760249
82   NaN  2018-07-01   -4.402019
          2018-08-01   -3.624764