Johnny
If I allow abandoned countries to be claimed by other players, one thing I could definitely see happening is a small country resigning and claiming an abandoned country if it's larger and wealthier.
I don't know if that's necessarily a bad thing, though. I suppose a player grabbing a larger country is more likely to keep playing than if he stayed as a small country.
I will agree that it could make the game more complex and dynamic, and for some people that would be more interesting, but the important question is "would that be more fun?". I can only see 3 scenarios in which a country would be abandoned in the first place:
A) The player has ended up on the losing side of a war to the point of not seeing a way to turn it around. Because of the long-term nature of GT, the actual loss (where you have no units and no income) might still be weeks away, but it is still obvious who the winner is going to be even if they have to start paying attention to another front. Who would really want to take over in this situation? At the very least, if this kind of take-over situation were allowed, the potential new regent ought to be given a brief of the current status of the country.
B) The player is simply trading up to a better country (larger, farther away from rivals, closer to friends...). I do not see any problems with allowing a new player to enter in this case, although potential new managers might appreciate knowing that this is a low-problem (if likely smaller) state. Even so, you might want to eliminate the country if it has not reached a certain minimum size.
C) The player is bored and quit. Their country may have no problems at all, but may also be of significant size, in an alliance, or otherwise pose a significant hazard to its immediate neighbors if suddenly under new management (especially if now run by a RL friend or spy of said neighbors).
As such, if take-overs are permitted, I would suggest two features be included along with that:
#1) I would suggest a simple tally of the number of attacks received in the past day, past week, and past month, and who they were by, as well as treaties (since we can already see alliances). This would permit a new player new ruler to enter the situation knowing who the countries current friends and enemies are.
#2) Drop the country into a state of anarchy lasting a minimum of at least a week, and continuing until the country is under new management or has had X losses (50% territory, capital, *shrug*). During this state of anarchy, the country cannot be taken over, is removed from any alliance, all its treaties are dropped, its units will not move (though they will defend themselves), and everyone in the world is notified that the country is in anarchy. This would give the state's neighbors time to adjust defences, make a land grab, or talk with potential takers.
The suggestions themselves might not be the best, but the point is that a truly new entrant should have some idea of what they are jumping into, and there should be some limited protection against sudden back-stabbing by the new management of a neighboring state.