diff --git a/Lib/test/test_ssl.py b/Lib/test/test_ssl.py
index 00d5eff..fbd0131 100644
--- a/Lib/test/test_ssl.py
+++ b/Lib/test/test_ssl.py
@@ -4464,11 +4464,18 @@ def msg_cb(conn, direction, version, content_type, msg_type, data):
                     '(certificate required|EOF occurred)'
                 ):
                     # receive CertificateRequest
-                    self.assertEqual(s.recv(1024), b'OK\n')
+                    data = s.recv(1024)
+                    if not data:
+                        raise ssl.SSLError(1, "EOF occurred")
+                    self.assertEqual(data, b'OK\n')
+
                     # send empty Certificate + Finish
                     s.write(b'HASCERT')
+
                     # receive alert
-                    s.recv(1024)
+                    data = s.recv(1024)
+                    if not data:
+                        raise ssl.SSLError(1, "EOF occurred")
 
     def test_pha_optional(self):
         if support.verbose:
diff --git a/Misc/NEWS.d/next/Tests/2021-06-02-17-41-42.bpo-43921.xP7yZ4.rst b/Misc/NEWS.d/next/Tests/2021-06-02-17-41-42.bpo-43921.xP7yZ4.rst
new file mode 100644
index 0000000..83146c7
--- /dev/null
+++ b/Misc/NEWS.d/next/Tests/2021-06-02-17-41-42.bpo-43921.xP7yZ4.rst
@@ -0,0 +1,2 @@
+Fix test_pha_required_nocert() of test_ssl: catch two more EOF cases (when
+the ``recv()`` method returns an empty string). Patch by Victor Stinner.