bpo-35926 and fb7e7505ed1337bf40fa7b8b68317d1e86675a86 introduced code that is triggered resource errors and unhandled exceptions. It has been bothering me for a while but I could never pin point the issue. Victor's and Hai's commits 
e80697d687b6 and 73ea54620a6f seem to be related, too.

I don't understand the purpose of the test changes in fb7e7505ed1337bf40fa7b8b68317d1e86675a86. The commit looks wrong to me. Could you please take a look?
 
$ ./python -X tracemalloc=10 -m test test_ssl
0:00:00 load avg: 1.37 Run tests sequentially
0:00:00 load avg: 1.37 [1/1] test_ssl
/home/heimes/dev/python/cpython/Lib/test/support/threading_helper.py:209: ResourceWarning: unclosed <ssl.SSLSocket fd=5, family=AF_INET, type=SOCK_STREAM, proto=0, laddr=('127.0.0.1', 32937), raddr=('127.0.0.1', 60292)>
  del self.thread
Object allocated at (most recent call last):
  File "/home/heimes/dev/python/cpython/Lib/threading.py", lineno 948
    self._bootstrap_inner()
  File "/home/heimes/dev/python/cpython/Lib/threading.py", lineno 990
    self.run()
  File "/home/heimes/dev/python/cpython/Lib/test/test_ssl.py", lineno 2404
    if not self.wrap_conn():
  File "/home/heimes/dev/python/cpython/Lib/test/test_ssl.py", lineno 2331
    self.sslconn = self.server.context.wrap_socket(
  File "/home/heimes/dev/python/cpython/Lib/ssl.py", lineno 513
    return self.sslsocket_class._create(
  File "/home/heimes/dev/python/cpython/Lib/ssl.py", lineno 1028
    self = cls.__new__(cls, **kwargs)

$ ./python -W "error::ResourceWarning" -m test test_ssl
0:00:00 load avg: 1.24 Run tests sequentially
0:00:00 load avg: 1.24 [1/1] test_ssl
Warning -- Unraisable exception
Exception ignored in: <ssl.SSLSocket fd=5, family=AF_INET, type=SOCK_STREAM, proto=0, laddr=('127.0.0.1', 49843), raddr=('127.0.0.1', 39420)>
Traceback (most recent call last):
  File "/home/heimes/dev/python/cpython/Lib/test/support/threading_helper.py", line 209, in __exit__
    del self.thread
ResourceWarning: unclosed <ssl.SSLSocket fd=5, family=AF_INET, type=SOCK_STREAM, proto=0, laddr=('127.0.0.1', 49843), raddr=('127.0.0.1', 39420)>
test_ssl failed (env changed)

Duplicate of bpo-37322 that I reported at 2019-06-17.

Thanks Victor, let's handle the issue in bpo-37322 instead.