If you're a Senior, I believe you can seize control of the Group as soon as the 7 days are up. If you are an Anbu or Elite, I believe in costs Coupons/Ingots to do the same thing.

I believe it's a first-come, first-serve basis. So once your current, inactive leader's offline time reaches 7 days, the seniors will have an option to impeach the leader. Whichever Senior does this first will assume control of the group and the other seniors will remain in their respective roles.

Source: http://forum.naruto.oasgames.com/en/forum.php?mod=redirect&goto=findpost&ptid=2786&pid=16095&fromuid=20658