Don't forget that there is a delay between being informed that X has destroyed Y, and Y be really out of the game.
The labels on your left tells you the information before a civilization is actually destroyed, can not be contacted, and is removed from display: if you pay attention to the messages (red labels), and see that a civ is destroyed, go right away to the diplomacy screen, and you will see this "destroyed" civ still present.
Hopefully you can engage in a trade - if you have not done so before -. It is time for a maximum of trades with them, as, as soon as the turn is finished and GNN gives the news, they won't be visible in any screen.
they are NOT removed from your saved game. If you had treaties with them (ex. open), when the treaty expires after 50 turns, you will still receive a warning in the left labels (yellow I think)...
Treaties, and some other gameplay data still remains. This is also why you cannot create twice a civ, by instance: a commonwealth civ, destroyed, and recreated later. You cannot use the same logo/data.
It can be annoying as, if you make an exploration treaty with a civ and it is destroyed next turn, you have to wait 49 turns before being able to do another treaty ! (limit is 1)