AIs rarely give a decent city, but they sure will ask for one.
In a recent MP game, India was abandonded very early in the game (not because the player was about to lose, no war had been declared - probably just an 'exit game = regenerate map' thinking, inconsiderate noob. Well, later, a player was hiding in Indian territory to heal after hitting me and India would not give me open borders! I had done nothing to them! I had to declare on India twice to go after healing troops during this long conflict. Well, as I finished mopping up the player's field army and taking his cities, another player hit me. Things were not going well. Then, India declared on me! and sent knights (Ghandi was tech leader). Just when all was nearly lost, another abandoned/now AI civ (Fredrick) finally agreed to declare on Japan (the player about to beat me) - for all the gold I had been saving for 30 turns at 0% research to get him to do it. To boost my last chance - psychological warfare -, I needed peace with India. I got it, but it cost me the better of my 2 remaining cities (I was left with only my tundra city). The Japan player saw Germany declare on him and India make peace with me in the same turn (just minutes before his final wave would have finished me for sure). He despaired and agreed to call it a draw! A draw?! Hah, in my mind, I won that one.