Indefinite deferral of a game

I was playing a friend the other day & he got busy and had to go before the game was finished. It felt unsporting to make him resign. I think it'd be nice to have a feature that allowed a game (mutually agreed upon) to change from a timed game into a correspondence game. If possible, how could abuse of the feature be prevented?

I think that the player who would otherwise have lost would have to lose rating points from their timed rating, and the following correspondence game would have to be unrated.
Also, I think that it would be necessary for both players to have to toggle an option to "turn this into a correspondence game on request" prior to the commencement of the original game.

#2: Implementing what you said in the first paragraph would be equal to having the player resign and then a From Position game continued.

A) Similar to an "Offer Draw" button, could be a "Remove clock" button that switches the game over to the correspondence page and gives a one move per day limit. One can simply refuse to "Remove clock" as easily as one refuses a draw.

B) Have another increment in the "Add Time" button instead of 15 seconds, maybe 2 hours or something. This would then tie-up your only allowable clock game on the site and then you couldn't play another timed game until that one was finished.