What one end of a stream reports to the server: one report per stream, and only a stream that played has a position worth saving.

Every end posts to the same stopped endpoint, and the stop does more than save the position: it stops the session's transcode and releases a Live TV live stream this session reported playing (one it never did is released by a close instead, see endClosesLiveStream). So a stream that never played still reports its end, marked Failed. Jellyfin then skips only the user-data write (its OnPlaybackStopped, 10.7.7 through 12.1), where an unmarked stop would save the position the player read before its first frame, usually 0, over the resume point (#969).

the stopped its stop raises is not the report

Whether this end releases the stream's Live TV live stream with a close by id rather than with its stop. Exactly one of the two must release it: each release drops one consumer, and a second one, on a stream the server shares between viewers, ends another viewer's stream.

A live stream that never reported its start (a direct play that failed over to transcode, a restart that ended at once, an error before the first frame) cannot rely on its stop, because what the server does with that stop depends on its version and on who else is watching: 10.7–10.10 always release, 10.11 never does (it releases only a session linked by a start or progress report, jellyfin#13220), and 12.x does only while no other session is linked (jellyfin#17178). So the close releases it, and the stop does not name the stream (liveStreamReportFields), which leaves it alone on every version. jellyfin-kodi ends every live stream the same way.

A stream that did report its start is released by its stop, as the server expects, and never closed here as well.

The Live TV fields a playback report carries. Every report names the media source, and every report names the live stream except the end of one that a close releases (endClosesLiveStream): a stop naming it would release it a second time on the servers that act on it.