BUG: regression for 1.3.0: saving a dataframe with the "pickle" package using pandas 1.2.5 would not open with "pickle" again with pandas 1.3.0
- [x] I have checked that this issue has not already been reported.

- [x] I have confirmed this bug exists on the latest version of pandas.

- [ ] (optional) I have confirmed this bug exists on the master branch of pandas.

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**Note**: Please read [this guide](https://matthewrocklin.com/blog/work/2018/02/28/minimal-bug-reports) detailing how to provide the necessary information for us to reproduce your bug.

#### Code Sample, a copy-pastable example

I created a notebook here to illustrate the issue

https://colab.research.google.com/drive/1por9_BTeLYvZxNzLOBv_jIsFh44mnz4N?usp=sharing

Main error message:

```
/usr/local/lib/python3.7/dist-packages/pandas/_libs/internals.pyx in pandas._libs.internals.BlockManager.__cinit__()

TypeError: __cinit__() takes at least 2 positional arguments (0 given)
```

#### Problem description

Dataframes saved with pandas 1.2.5 and "pickle" are no longer loadable with pandas 1.3.0

Related to #42343

#### Expected Output

#### Output of ``pd.show_versions()``

<details>

INSTALLED VERSIONS
------------------
commit           : f00ed8f47020034e752baf0250483053340971b0
python           : 3.7.10.final.0
python-bits      : 64
OS               : Linux
OS-release       : 5.4.104+
Version          : #1 SMP Sat Jun 5 09:50:34 PDT 2021
machine          : x86_64
processor        : x86_64
byteorder        : little
LC_ALL           : None
LANG             : en_US.UTF-8
LOCALE           : en_US.UTF-8

pandas           : 1.3.0
numpy            : 1.19.5
pytz             : 2018.9
dateutil         : 2.8.1
pip              : 19.3.1
setuptools       : 57.0.0
Cython           : 0.29.23
pytest           : 3.6.4
hypothesis       : None
sphinx           : 1.8.5
blosc            : None
feather          : 0.4.1
xlsxwriter       : None
lxml.etree       : 4.2.6
html5lib         : 1.0.1
pymysql          : None
psycopg2         : 2.7.6.1 (dt dec pq3 ext lo64)
jinja2           : 2.11.3
IPython          : 5.5.0
pandas_datareader: 0.9.0
bs4              : 4.6.3
bottleneck       : 1.3.2
fsspec           : None
fastparquet      : None
gcsfs            : None
matplotlib       : 3.2.2
numexpr          : 2.7.3
odfpy            : None
openpyxl         : 2.5.9
pandas_gbq       : 0.13.3
pyarrow          : 3.0.0
pyxlsb           : None
s3fs             : None
scipy            : 1.4.1
sqlalchemy       : 1.4.18
tables           : 3.4.4
tabulate         : 0.8.9
xarray           : 0.18.2
xlrd             : 1.1.0
xlwt             : 1.3.0
numba            : 0.51.2


</details>
