I have a friend game that I naively made 15 frames long that will never end. I would appreciate the ability to end such games before completion so that I can see its work.
Alternatively, when new games (either public or private) are created, the OP could set an optional "timeout" period after which the game would expire and whatever frames are completed are displayed.
A default of perhaps 2 weeks could be set, with options for 1 week, 4 weeks or indefinite. This way, some games and people's hard work are not forever caught in limbo!