In-memory to_pickle leads to I/O error
#### Code Sample
```
# import libraries
import pandas as pd
import io

# show version
print(pd.__version__)
# 0.25.2

# create example dataframe
df = pd.DataFrame({"A": [1, 2, 3, 4], "B": [5, 6, 7, 8]})

# create io-stream to act as surrogate file
stream = io.BytesIO()

# since the compression cannot be inferred from the filename, it has to be set explicitly.
df.to_pickle(stream, compression=None)

# stream.getvalue() can be used as binary load in an api call to save the dataframe in the cloud
print(stream.getvalue())
'''
correct output pandas version 0.24.1:
b'\x80\x04\x95\xe2\x02\x00\x00\x00\x00\x00\x00\x8c\x11pandas.core.frame\x94\x8c\tDataFrame\x94\x93\x94)\x81\x94}\x94(\x8c\x05_data\x94\x8c\x1epandas.core.internals.managers\x94\x8c\x0cBlockManager\x94\x93\x94)\x81\x94(]\x94(\x8c\x18pandas.core.indexes.base\x94\x8c\n_new_Index\x94\x93\x94h\x0b\x8c\x05Index\x94\x93\x94}\x94(\x8c\x04data\x94\x8c\x15numpy.core.multiarray\x94\x8c\x0c_reconstruct\x94\x93\x94\x8c\x05numpy\x94\x8c\x07ndarray\x94\x93\x94K\x00\x85\x94C\x01b\x94\x87\x94R\x94(K\x01K\x02\x85\x94h\x15\x8c\x05dtype\x94\x93\x94\x8c\x02O8\x94K\x00K\x01\x87\x94R\x94(K\x03\x8c\x01|\x94NNNJ\xff\xff\xff\xffJ\xff\xff\xff\xffK?t\x94b\x89]\x94(\x8c\x01A\x94\x8c\x01B\x94et\x94b\x8c\x04name\x94Nu\x86\x94R\x94h\r\x8c\x19pandas.core.indexes.range\x94\x8c\nRangeIndex\x94\x93\x94}\x94(h(N\x8c\x05start\x94K\x00\x8c\x04stop\x94K\x04\x8c\x04step\x94K\x01u\x86\x94R\x94e]\x94h\x14h\x17K\x00\x85\x94h\x19\x87\x94R\x94(K\x01K\x02K\x04\x86\x94h\x1e\x8c\x02i8\x94K\x00K\x01\x87\x94R\x94(K\x03\x8c\x01<\x94NNNJ\xff\xff\xff\xffJ\xff\xff\xff\xffK\x00t\x94b\x89C@\x01\x00\x00\x00\x00\x00\x00\x00\x02\x00\x00\x00\x00\x00\x00\x00\x03\x00\x00\x00\x00\x00\x00\x00\x04\x00\x00\x00\x00\x00\x00\x00\x05\x00\x00\x00\x00\x00\x00\x00\x06\x00\x00\x00\x00\x00\x00\x00\x07\x00\x00\x00\x00\x00\x00\x00\x08\x00\x00\x00\x00\x00\x00\x00\x94t\x94ba]\x94h\rh\x0f}\x94(h\x11h\x14h\x17K\x00\x85\x94h\x19\x87\x94R\x94(K\x01K\x02\x85\x94h!\x89]\x94(h%h&et\x94bh(Nu\x86\x94R\x94a}\x94\x8c\x060.14.1\x94}\x94(\x8c\x04axes\x94h\n\x8c\x06blocks\x94]\x94}\x94(\x8c\x06values\x94h7\x8c\x08mgr_locs\x94\x8c\x08builtins\x94\x8c\x05slice\x94\x93\x94K\x00K\x02K\x01\x87\x94R\x94uaust\x94b\x8c\x04_typ\x94\x8c\tdataframe\x94\x8c\t_metadata\x94]\x94ub.'

erroneous output pandas version 0.25.2:
Traceback (most recent call last):
  File "C:/Projects/bug_report/report_bug.py", line 20, in <module>
    print(stream.getvalue())
ValueError: I/O operation on closed file.
'''
```

#### Problem description

Occasionally I would like to save Pandas dataframes in the cloud. This can be done through api-calls in which the dataframe is uploaded as binary content. The binary content can be created through providing a io.BytesIO stream to the pandas.to_pickle method. Subsequently the binary content can be obtained by the method getvalue from io.BytesIO. This works perfectly in pandas version 0.24.1. However, when updating to pandas version 0.25.2, this ceases to work. Apparently the io.BytesIO stream gets now closed in the pandas.to_pickle method and can no longer be accessed.

#### Expected Output
A binary string as produced in pandas version 0.24.1, see code example above

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

<details>

INSTALLED VERSIONS
------------------
commit           : None
python           : 3.7.5.final.0
python-bits      : 64
OS               : Windows
OS-release       : 10
machine          : AMD64
processor        : Intel64 Family 6 Model 158 Stepping 10, GenuineIntel
byteorder        : little
LC_ALL           : None
LANG             : None
LOCALE           : None.None
pandas           : 0.25.2
numpy            : 1.17.3
pytz             : 2019.3
dateutil         : 2.8.1
pip              : 19.3.1
setuptools       : 41.6.0.post20191030
Cython           : None
pytest           : None
hypothesis       : None
sphinx           : None
blosc            : None
feather          : None
xlsxwriter       : None
lxml.etree       : None
html5lib         : None
pymysql          : None
psycopg2         : None
jinja2           : None
IPython          : None
pandas_datareader: None
bs4              : None
bottleneck       : None
fastparquet      : None
gcsfs            : None
lxml.etree       : None
matplotlib       : None
numexpr          : None
odfpy            : None
openpyxl         : None
pandas_gbq       : None
pyarrow          : None
pytables         : None
s3fs             : None
scipy            : None
sqlalchemy       : None
tables           : None
xarray           : None
xlrd             : None
xlwt             : None
xlsxwriter       : None
None

</details>
