For games that you can no longer play (ie. dead MMOs, multiplayer game where the servers went dark, or some other threshold), how do we handle the existing questions? Do we want to keep them around, even though they can no longer help anyone?
Depends on your definition of "no longer help anyone".
First, I think that most of the time if someone asks a question, then they probably have some use for it. So, someone asked a question about a MMO that just went offline? Are you sure that they are not playing on a private server (there are a few rare case where that should be legal and even approved by the original company)? They may have a perfectly legal reason to ask, even out of curiosity, even if you assume they don't.
Second and probably more important... Who said that the answer would not be interesting even if the game is no longer accessible?? You may have a point that a no-longer playable game is a game no one can make new discoveries about, but... the information one seeks could have existed far before it became impossible to do more research.
Take for example Final Fantasy XI. Even if the rumors about a shut down had been true and the game was no longer playable now, a question like "Did players even discovered what was the intended way to beat Absolute Virtue (1)" would be still relevant. In the same way, even int the case of a shut down of the original Guild Wars online servers questions about the lore and plot would still be relevant for players playing the sequel.
Probably, it is better to focus on an higher level problem. "Can the question still be answered?". If the shut down made answering the question impossible, there is some reasoning to close it, but if the question can still be answered even when the game is no longer about, perhaps it would make sense to leave it open.
1: yep, that is the boss that was changed multiple times by the developers because players "didn't beat it the way we have intended", often removing any loot the players had got in the process...