i would also like an option like that and maybe reward 1 min or so to the opponent but definitely being able to finish a game (of course the opponent have to agree with both thing thou)
continue/finish game

This option should have been added ages ago. Not hard at all to do. I’d much rather finish a game than a rematch. I rarely ever rematch unless I lose to a higher ranked player, and they request one. Even then it’s a 50/50 chance on time accepting the rematch, but if there was the option to play through and finish the game after the clock has ran out I’d be all for that depending on how close the game is.
I really think you should incorporate a button to click to continue a game with your opponent that has run out of time. This will not change who won or lost, as the one who ran out of time loses. I would just really enjoy and like to sometimes finish playing out a really good and close game against an opponent or friend. Sometimes your in the final stage of the game and you or opponent runs out of time, and you just think to yourself man I really wish I could have finished the game against him it was a really fun and good match.
So please allow for this, it would be really great. Who ever ran out of time gets the loss, but you can redeem yourself with a possible unofficial win.
I know you can do a rematch, but Id really prefer to finish the game than have a rematch. It will also help improve beginners game cause they can also take their time with their moves cause there won’t be a timer anymore either, and get them more use to playing with a clock.