In the instance of a position that may wind up being a draw, a suggestion for that would be the following:

For a draw that is offered, if it is declined, the 40 Move Rule would be invoked and, if necessary, an option would pop up to contact someone (i.e. Fencer) to watch the game and see if a drawn position would show up before the limit is up. Thus, a timer would be set that tracks each move and list how many moves are left before the draw is declared automatically. Either way, a drawn game would end and would be credited in the respective tournament (this could work in Chess, too, with the 50 Move Rule).

I would see that function as something to be helpful in such situations and would be flexible enough for someone to declare a game finished and then, the option would have a box for that person to message Fencer with their reason for ending the game. Thus, Fencer would have the available information to make a judgemental decision to either grant or deny that request.