A long time ago that was something they did in Live. I haven't read all the posts about it but I imagine they stopped doing that due the fact that the vast majority of game were never finished. It is just better to conclude the game immediately and calculate ratings.
Ability to adjourn a game
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I have played other sites where there was adjourned games. In the beginning there were a lot of games never finished. Later they implemented some judging (either by human or AI) to give victory to each side after some days if not resumed. And if 2 players got online with adjourned games they were automatically paired. But I think is faster, easier to account victories and ratings instantly.
Every once in a while you're in a game and something pops up in life and you need to attend to it and can't continue the game. Rather than accept a loss, many players have a connection to their rating, and I get draw offers... But then there's this draw death factor to chess where it usually favors one player or another. Also the reasoning behind the draw offer, such as if it's very early in the game, can require an explanation. A handful of players have poor communication and this just leads to misunderstandings due to their inability to communicate properly and explain their situation, or maybe they can explain it but don't have time as a luxury to explain it very well....
I was thinking would it be possible to add an "adjourn this game" sort of feature. Sort of like if the game were abandoned, but both players can agree to adjourn it. This would also help in situations where the other player has chat disabled, etc and they don't want to have to deal with draw offers. While personally I don't care about my rating, it just catches up with me over time anyways, I know many players take their rating very serious. And I think it would be great if there were an option to agree to "cancel" a game if both players decide to.