Eventually, every shiritori game gets to a point where there are no legal words left to play. Players should be able to flag this situation so that the game can end without waiting for a timeout or manual admin check.
Optional: add scoring/penalties.
If the player is correct, and no legal plays remain, give them points equivalent to playing a word. If they are incorrect, and there is a legal play, show them a legal play, but don’t allow them to play it. Or maybe make the play for them and deduct the equivalent number of points (times a penalty factor, if desired).
There are no manual checks - it is automated, and it runs pretty frequently (every 5 minutes). On the flip side, I am not sure that users (even if it requires multiple "marks") are going to generally be equipped to check as to whether or not it's at an end - I could easily say "well, I can't think of any, let's end it). Ultimately, though, I do not see a situation where humans will be a better judge of it ending than the computer (either in its current state, or with some updates).
That being said, there was an update to the backend of renshuu (that handles, among other things, the checking), so it's possible that there were issues with how quickly the games were ended.
義務 has been up on 2-character kanji shiritori since I posted this. I could be wrong, but I don’t believe any legal plays remain. If you think there’s a legal play, please play it.
It's been fixed! As to what was causing it, the periodic scanner was not filtering the words correctly, and was allowing words that had been entered by users, but not verified (would not appear in the dictionary). The term happened to be 務省
Anyway, it's been fixed! If you ever see another shiritori round that seems "stuck", do let me know.