[Bugfix]Fix search start_index of stop_checker (vllm-project#13280)

Author: xu-song

vllm/engine/output_processor/stop_checker.py

@@ -113,7 +113,7 @@ def check_stop_strings(
             stop_string_len = len(stop_str)
             # Avoid searching already-searched text.
             stop_index = output_text.find(stop_str,
-                                          -new_char_count - stop_string_len)
+                                          1 - new_char_count - stop_string_len)
             if stop_index == -1:
                 continue