if not time-out is claimed during siege or tour...

Say a player has used his timebank in a siege game, or in a tournament game. And say that his opponent does not time him out. What happens? Will the game stand open, as "in progress", and keep the siege/tournament undecided?
Is there a way of end games if that situation happens? If so, for how long does the siege-queue /tournamentsplayers wait for that to happen?

They'll automatically be timed out - 2 days after timebank ends in a tournament and something like 10 days in a siege.