diff --git a/agent/codex_runtime.py b/agent/codex_runtime.py
index cdce3f87c1..44a35410f5 100644
--- a/agent/codex_runtime.py
+++ b/agent/codex_runtime.py
@@ -8,6 +8,7 @@ import contextvars
 import json
 import logging
 import os
+import threading
 import time
 from contextlib import suppress
 from types import SimpleNamespace
@@ -23,6 +24,8 @@ _codex_watchdog_state_var: contextvars.ContextVar[Any | None] = contextvars.Cont
     "codex_watchdog_state", default=None
 )
 
+_CODEX_POST_TERMINAL_DRAIN_TIMEOUT_SECONDS = 2.0
+
 
 def _call_guarded(fn: Callable | None, fail_msg: str, *fail_args: Any, args: tuple = (), kwargs: dict | None = None):
     """Invoke an optional display/debug callback; a buggy hook must never tear down the turn."""
@@ -981,15 +984,32 @@ def run_codex_stream(agent, api_kwargs: dict, client: Any = None, on_first_delta
     def _drain_for_finalizer(event_stream: Any) -> None:
         # ``final`` is already assembled; draining only lets Relay run its finalizer. A transport error
         # here must NOT discard the completed, already-billed response.
-        try:
-            for _ignored in event_stream:
-                pass
-        except (*transport_errors, _APIConnectionError) as exc:
-            if not isinstance(exc, transport_errors):
-                _log_failure(exc)
-            logger.warning("Codex Responses stream transport finalization failed after a terminal response was already "
-                           "received; returning the completed response instead of retrying. %s error=%s",
-                           agent._client_log_context(), exc)
+        drained = threading.Event()
+
+        def _drain() -> None:
+            try:
+                for _ignored in event_stream:
+                    pass
+            except (*transport_errors, _APIConnectionError) as exc:
+                if not isinstance(exc, transport_errors):
+                    _log_failure(exc)
+                logger.warning("Codex Responses stream transport finalization failed after a terminal response was already "
+                               "received; returning the completed response instead of retrying. %s error=%s",
+                               agent._client_log_context(), exc)
+            except Exception:
+                logger.debug("Codex Responses stream finalization failed after a terminal response", exc_info=True)
+            finally:
+                drained.set()
+
+        threading.Thread(target=_drain, name="codex-post-terminal-drain", daemon=True).start()
+        if drained.wait(_CODEX_POST_TERMINAL_DRAIN_TIMEOUT_SECONDS):
+            return
+        logger.warning(
+            "Codex Responses stream remained open %.1fs after a terminal response; closing it and returning the "
+            "completed response instead of retrying. %s",
+            _CODEX_POST_TERMINAL_DRAIN_TIMEOUT_SECONDS, agent._client_log_context(),
+        )
+        _close_event_stream(event_stream)
 
     def _close_event_stream(event_stream: Any) -> None:
         close_fn = getattr(event_stream, "close", None)  # None while connect never succeeded
diff --git a/tests/agent/test_run_agent_codex_responses.py b/tests/agent/test_run_agent_codex_responses.py
index 647a7b2c56..9ad2717662 100644
--- a/tests/agent/test_run_agent_codex_responses.py
+++ b/tests/agent/test_run_agent_codex_responses.py
@@ -1080,6 +1080,68 @@ def test_run_codex_stream_returns_terminal_response_when_post_terminal_drain_fai
     )
 
 
+def test_run_codex_stream_bounds_post_terminal_drain(monkeypatch):
+    """A relay that keeps SSE open after completion cannot discard the billed response."""
+    import threading
+    import time
+
+    import agent.codex_runtime as codex_runtime
+
+    agent = _build_agent(monkeypatch)
+    message_item = SimpleNamespace(
+        type="message",
+        status="completed",
+        content=[SimpleNamespace(type="output_text", text="All done.")],
+    )
+    usage = SimpleNamespace(input_tokens=10, output_tokens=6, total_tokens=16)
+    closed = threading.Event()
+
+    class _HeldOpenAfterTerminalStream:
+        def __init__(self):
+            self._events = iter([
+                SimpleNamespace(type="response.output_item.done", item=message_item),
+                SimpleNamespace(
+                    type="response.completed",
+                    response=SimpleNamespace(
+                        status="completed", usage=usage, id="resp_held_open",
+                    ),
+                ),
+            ])
+
+        def __iter__(self):
+            return self
+
+        def __next__(self):
+            try:
+                return next(self._events)
+            except StopIteration:
+                closed.wait(3.0)
+                raise
+
+        def close(self):
+            closed.set()
+
+    calls = {"count": 0}
+
+    def _fake_create(**kwargs):
+        calls["count"] += 1
+        return _HeldOpenAfterTerminalStream()
+
+    agent.client = SimpleNamespace(responses=SimpleNamespace(create=_fake_create))
+    monkeypatch.setattr(codex_runtime, "_CODEX_POST_TERMINAL_DRAIN_TIMEOUT_SECONDS", 0.01)
+
+    started = time.monotonic()
+    response = agent._run_codex_stream(_codex_request_kwargs())
+    elapsed = time.monotonic() - started
+
+    assert elapsed < 2.0
+    assert calls["count"] == 1
+    assert response.status == "completed"
+    assert response.usage is usage
+    assert response.id == "resp_held_open"
+    assert closed.wait(1.0)
+
+
 def test_run_conversation_codex_plain_text(monkeypatch):
     agent = _build_agent(monkeypatch)
     monkeypatch.setattr(agent, "_interruptible_api_call", lambda api_kwargs: _codex_message_response("OK"))