The procedure is this:

1) Ask the player playing the dying nation to set themselves to AI. Many players fail to do so simply because they don't realise they're meant to set their nations to AI when they want to stop playing. If you ask them to, there's a good chance they will.

2) If that fails, you need to either do it yourself, or ask some trusted member of the community to do it. The disadvantage of doing it yourself is that you will see the position of the dying nation and its neighbours, which is a bit dodgy. Finding someone else to do it is a hassle though. I recommend asking someone else from that game who's already been knocked out, or else someone random you've played with before. If you always ask me or Gandalf, we will go mad.

3) Having found someone to set the nation to AI, you need to get the player's turn to them. To do that, change the nation's e-mail address to that player's address, and request a turn resend from the main game page. They then need to open the turn up in Dominions, set the player to AI and e-mail the resulting 2h file back to the LlamaServer.

Phew!