diff --git a/src/proto/server/client.rs b/src/proto/server/client.rs
index 8d296eb..acaea6d 100644
--- a/src/proto/server/client.rs
+++ b/src/proto/server/client.rs
@@ -292,13 +292,14 @@ mod tests {
     // chance to send all of `outbound`.
     handle.shutdown();
 
-    // Check that the client returns the correct error.
+    // Check that the client returns the correct error, then stops running.
     assert!(inbound
       .next()
       .await
       .unwrap()
       .unwrap_err()
       .is_stream_closed());
+    assert!(inbound.next().await.is_none());
 
     server_task.await.unwrap().unwrap();
   }