I was wondering how other games handle this issue and discovered the following in old Raging Bulls post...
(...)
Regarding your suggestion, we thought about it, but the problem is exactly the one you mention. We cannot be certain that current score is a minimum number of points. It is possible that the score will be reduced with more moves. We try to standardise everything and I am afraid there is no way to be fair with everyone without complexifying the code overly (and increasing the development time and the likely of a bug). Our next game will have the same issue too.
So the only thing we can realistically really do is consider an unfinished game as equivalent to the worst possible performance (which is 1000 for Raging Bulls).
Always finish your games is the main advice here.
If the same strategy (assigning the worst possible performance) was used for HexRoller, it would explain my zero (0) though, with HexRoller, there is less opportunity to reduce one's score in future moves. Regardless, providing a way to override a really bad result (i.e. by resuming the game from point of interruption -- and perhaps only before another game is started) would still be my preferred solution.