diff --git a/tests/async_engine/test_async_llm_engine.py b/tests/async_engine/test_async_llm_engine.py
index bab42942d311f..a093a2b29278a 100644
--- a/tests/async_engine/test_async_llm_engine.py
+++ b/tests/async_engine/test_async_llm_engine.py
@@ -159,7 +159,8 @@ def should_do_global_cleanup_after_test(request) -> bool:
 
 
 @pytest.mark.asyncio(scope="module")
-async def test_asyncio_run(async_engine):
+@pytest.mark.parametrize("stop", [None, ["a stop string"]])
+async def test_asyncio_run(async_engine, stop):
 
     scheduler_config = await async_engine.get_scheduler_config()
     num_scheduler_steps = scheduler_config.num_scheduler_steps
@@ -169,6 +170,7 @@ async def run(prompt: str):
             temperature=0,
             max_tokens=32,
             min_tokens=32,
+            stop=stop,
         )
 
         output_count = 0
@@ -203,7 +205,8 @@ async def run(prompt: str):
 
 
 @pytest.mark.asyncio(scope="module")
-async def test_output_kinds(async_engine):
+@pytest.mark.parametrize("stop", [None, ["a stop string"]])
+async def test_output_kinds(async_engine, stop):
     """Test that output_kind works as expected and that
     results are equivalent across different kinds."""
 
@@ -214,6 +217,7 @@ async def test_output_kinds(async_engine):
         temperature=0,
         max_tokens=32,
         min_tokens=32,
+        stop=stop,
     )
 
     async def run(prompt: str, kind: RequestOutputKind):
@@ -229,6 +233,8 @@ async def run(prompt: str, kind: RequestOutputKind):
             final_output = output
 
         assert final_output is not None
+        assert final_output.finished
+
         return (final_output.prompt_token_ids,
                 final_output.outputs[0].token_ids,
                 final_output.outputs[0].text, output_count)
@@ -241,16 +247,18 @@ async def run_deltas(prompt: str):
         output_tokens: List[int] = []
         output_text = ""
         output_count = 0
+        final_output = None
         async for output in async_engine.generate(prompt,
                                                   params,
                                                   request_id=uid()):
             token_ids = output.outputs[0].token_ids
             text = output.outputs[0].text
+            final_output = output
 
             # Ensure we get prompt ids iff we haven't yet received output tokens
             if output_tokens:
                 assert 1 <= len(token_ids) <= num_scheduler_steps
-                assert text
+                assert stop or text
                 assert not output.prompt_token_ids
             else:
                 assert output.prompt_token_ids
@@ -260,6 +268,10 @@ async def run_deltas(prompt: str):
             output_text += text
 
             output_count += 1
+
+        assert final_output is not None
+        assert final_output.finished
+
         return prompt_tokens, output_tokens, output_text, output_count
 
     results = await asyncio.gather(
@@ -291,7 +303,8 @@ async def run_deltas(prompt: str):
 
 
 @pytest.mark.asyncio(scope="module")
-async def test_cancellation(async_engine):
+@pytest.mark.parametrize("stop", [None, ["a stop string"]])
+async def test_cancellation(async_engine, stop):
     scheduler_config = await async_engine.get_scheduler_config()
     num_scheduler_steps = scheduler_config.num_scheduler_steps
 
@@ -299,6 +312,7 @@ async def test_cancellation(async_engine):
         temperature=0,
         min_tokens=13,
         max_tokens=13,
+        stop=stop,
     )
 
     stop_at = 5 if num_scheduler_steps == 1 else 1
@@ -319,7 +333,8 @@ async def test_cancellation(async_engine):
 
 
 @pytest.mark.asyncio(scope="module")
-async def test_delayed_generator(async_engine):
+@pytest.mark.parametrize("stop", [None, ["a stop string"]])
+async def test_delayed_generator(async_engine, stop):
     scheduler_config = await async_engine.get_scheduler_config()
 
     if scheduler_config.num_scheduler_steps != 1:
@@ -329,6 +344,7 @@ async def test_delayed_generator(async_engine):
         temperature=0,
         min_tokens=10,
         max_tokens=10,
+        stop=stop,
     )
 
     stream = async_engine.generate("test3", sampling_params, request_id=uid())
diff --git a/vllm/sequence.py b/vllm/sequence.py
index 98a8b73586062..07ceccf123541 100644
--- a/vllm/sequence.py
+++ b/vllm/sequence.py
@@ -477,7 +477,9 @@ def get_output_text_to_return(self, buffer_length: int,
         if not delta:
             return self.output_text[:-buffer_length] if truncate else (
                 self.output_text)
-        length = len(self.output_text) - buffer_length
+        length = len(self.output_text)
+        if truncate:
+            length -= buffer_length
         last_offset = self._last_output_text_offset
         if last_offset < length:
             self._last_output_text_offset = length