diff --git a/ssl/ssl_buffer.cc b/ssl/ssl_buffer.cc
index d73055f..2ca14ef 100644
--- a/ssl/ssl_buffer.cc
+++ b/ssl/ssl_buffer.cc
@@ -232,6 +232,7 @@
       return 1;
 
     case ssl_open_record_close_notify:
+      ssl->s3->rwstate = SSL_ERROR_ZERO_RETURN;
       return 0;
 
     case ssl_open_record_error:
diff --git a/ssl/ssl_lib.cc b/ssl/ssl_lib.cc
index 56bc5c2..3b06bf0 100644
--- a/ssl/ssl_lib.cc
+++ b/ssl/ssl_lib.cc
@@ -1319,7 +1319,7 @@
   }
 
   if (ret_code == 0) {
-    if (ssl->s3->read_shutdown == ssl_shutdown_close_notify) {
+    if (ssl->s3->rwstate == SSL_ERROR_ZERO_RETURN) {
       return SSL_ERROR_ZERO_RETURN;
     }
     // An EOF was observed which violates the protocol, and the underlying
@@ -2578,7 +2578,13 @@
   return CRYPTO_get_ex_data(&ctx->ex_data, idx);
 }
 
-int SSL_want(const SSL *ssl) { return ssl->s3->rwstate; }
+int SSL_want(const SSL *ssl) {
+  // Historically, OpenSSL did not track |SSL_ERROR_ZERO_RETURN| as an |rwstate|
+  // value. We do, but map it back to |SSL_ERROR_NONE| to preserve the original
+  // behavior.
+  return ssl->s3->rwstate == SSL_ERROR_ZERO_RETURN ? SSL_ERROR_NONE
+                                                   : ssl->s3->rwstate;
+}
 
 void SSL_CTX_set_tmp_rsa_callback(SSL_CTX *ctx,
                                   RSA *(*cb)(SSL *ssl, int is_export,
diff --git a/ssl/ssl_test.cc b/ssl/ssl_test.cc
index 1db97a9..9f488d5 100644
--- a/ssl/ssl_test.cc
+++ b/ssl/ssl_test.cc
@@ -8450,6 +8450,11 @@
   EXPECT_EQ(ret, 0);
   EXPECT_EQ(SSL_get_error(client.get(), ret), SSL_ERROR_ZERO_RETURN);
 
+  // Further calls to |SSL_read| continue to report |SSL_ERROR_ZERO_RETURN|.
+  ret = SSL_read(client.get(), buf, sizeof(buf));
+  EXPECT_EQ(ret, 0);
+  EXPECT_EQ(SSL_get_error(client.get(), ret), SSL_ERROR_ZERO_RETURN);
+
   // Although the client has seen close_notify, it should continue to report
   // |SSL_ERROR_SYSCALL| when its writes fail.
   ret = SSL_write(client.get(), data, sizeof(data));
@@ -8457,6 +8462,22 @@
   EXPECT_EQ(SSL_get_error(client.get(), ret), SSL_ERROR_SYSCALL);
   EXPECT_TRUE(write_failed);
   write_failed = false;
+
+  // Cause |BIO_write| to fail with a return value of zero instead.
+  // |SSL_get_error| should not misinterpret this as a close_notify.
+  //
+  // This is not actually a correct implementation of |BIO_write|, but the rest
+  // of the code treats zero from |BIO_write| as an error, so ensure it does so
+  // correctly. Fixing https://crbug.com/boringssl/503 will make this case moot.
+  BIO_meth_set_write(method.get(), [](BIO *, const char *, int) -> int {
+    write_failed = true;
+    return 0;
+  });
+  ret = SSL_write(client.get(), data, sizeof(data));
+  EXPECT_EQ(ret, 0);
+  EXPECT_EQ(SSL_get_error(client.get(), ret), SSL_ERROR_SYSCALL);
+  EXPECT_TRUE(write_failed);
+  write_failed = false;
 }
 
 // Test that |SSL_shutdown|, when quiet shutdown is enabled, simulates receiving