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And the original agreement might have said that the balance transfer rate wouldn't last past a cancellation, but not in so many words. It might have spelled out various cases where a balance transfer rate would end (an obvious example case would be missing a payment), and in that list might have buried something which, if examined carefully, includes the situation of cancelling the card.

So I would suggest the OP both look over the original terms of the balance transfer very carefully, and also ask Citi about it and get it in writing (or else hang up, call again, and ask several different Citi customer service people and see if they all say the same thing).

Meanwhile, if the card isn't cancelled, and the annual fee is billed, is there any chance that interest (at a much higher rate than 0%!) will be charge on the annual fee if the statement with the annual fee is not paid off in full? There's nothing the say that a bank has to apply payment on the card in the order that you prefer; they can apply part of the payment that you think is the annual fee to the 0% balance, and now some of the annual fee carries over to the next cycle, and then gets hit with the "full" interest rate, right?

(I haven't dared try doing a balance transfer on an annual fee card. But I do have two separate 0% balance transfers on the same card, one ending months before the other, but if I try to pay off the one that ends first by itself, I can't, because any extra amount I pay in a given month, the bank applies that to the transfer that ends last, not the transfer that ends first! So I'll have to pay both of them off by the time the first one expires, it seems. So it's clear to me that a bank may not apply payments in the order you wish it would.)