I made the mistake of entering a 7 days timeout tournament which started in February 2004,I'd never imagine it would have lasted so long, and there are some rounds to play before I'll see the end of it...................
I'll never repeat that mistake!
I don't think you can really change the rules mid-tournament, which is effectively what you're asking. Both players must be moving within the allotted time, otherwise they'd be timed out.
At least with tournaments you don't have the problem of the clan leagues, where people can leave the site and leave a game in limbo. Hmm, actually, maybe in some cases if the people weren't moving at all the game would be over QUICKER! 😉
Having said all that, you do have to wonder why this game is still going. It would be different if a stalemate/draw would help someone advance to the next round, but (a) a draw is an incredibly remote hope and (b) it won't make any difference to who progresses and (c) there's not even that many ratings points at stake.