diff --git a/yt_dlp/downloader/fragment.py b/yt_dlp/downloader/fragment.py
index 7b213cd5f..24f4ec959 100644
--- a/yt_dlp/downloader/fragment.py
+++ b/yt_dlp/downloader/fragment.py
@@ -137,7 +137,12 @@ class FragmentFD(FileDownloader):
         if fragment_info_dict.get('filetime'):
             ctx['fragment_filetime'] = fragment_info_dict.get('filetime')
         ctx['fragment_filename_sanitized'] = fragment_filename
-        return True, self._read_fragment(ctx)
+        try:
+            return True, self._read_fragment(ctx)
+        except FileNotFoundError:
+            if not info_dict.get('is_live'):
+                raise
+            return False, None
 
     def _read_fragment(self, ctx):
         down, frag_sanitized = self.sanitize_open(ctx['fragment_filename_sanitized'], 'rb')