There are a few ways of dealing with time-outs in multi-player games. One could implement games where "pass" is a valid move (not necessarely a good move), and someone timing out means the person passed. Or, instead of a pass, there's a default move, or the previous move is repeated (ponds work that way, don't they?) For instance, an implementation of 'Uno' might cause a timing-out player to draw a card from the draw-stack, as if (s)he couldn't play a card from their hand.

There are also games where players are eliminated one-by-one, monopoly or ludo are classical examples of such games. In such games, time-outs can be dealt with in the same way as they are dealt with currently: elimination of the player timing out.

But there are a lot of games left I don't see a solution for.