diff --git a/src/claude_code_api/stream.py b/src/claude_code_api/stream.py
index 5f8b944..9e2fdc3 100644
--- a/src/claude_code_api/stream.py
+++ b/src/claude_code_api/stream.py
@@ -377,7 +377,12 @@ class StreamClaudeProcess:
                 await self._queue.put(record)
         finally:
             self._eof = True
-            await self._queue.put(None)
+            # `put_nowait`, not `await put`: this runs in a `finally`
+            # that a shutdown-time cancellation may have entered, and an
+            # unbounded queue never blocks anyway. Awaiting here would
+            # risk swallowing the sentinel and leaving a turn generator
+            # parked on `next_record()` forever.
+            self._queue.put_nowait(None)
 
     async def _read_stderr(self) -> None:
         proc = self._proc
@@ -456,11 +461,19 @@ class StreamClaudeProcess:
     # ---- shutdown -----------------------------------------------------
 
     async def terminate(self, *, grace: float = 5.0) -> int | None:
-        """SIGTERM → wait up to `grace` seconds → SIGKILL ladder."""
+        """Close stdin → SIGTERM → wait up to `grace` → SIGKILL ladder.
+
+        Closing stdin first is the protocol's own goodbye: headless
+        claude exits on EOF, so a healthy process usually never sees the
+        signals at all.
+        """
         proc = self._proc
         if proc is None:
             return None
         if proc.returncode is None:
+            with contextlib.suppress(Exception):
+                if proc.stdin is not None and not proc.stdin.is_closing():
+                    proc.stdin.close()
             signal_group(proc.pid, signal.SIGTERM)
             with contextlib.suppress(TimeoutError):
                 await asyncio.wait_for(proc.wait(), timeout=grace)