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if by "i paid up and closed my credit card" you mean you paid off the balance that was showing at that moment, but you were still accruing interest charges that didn't hit your account until the end of the monthly cycle (after you closed your account) then yes, you owed the interest at that point.
and if you never paid the interest, then yes, they can hit you with late fees on the unpaid amount.
note that when you close a credit card account, that doesn't mean that they agree the balance is zero and no further charges will accrue. they're supposed to warn you to check your next statement and pay off any final interest charges and/or fees (and also to make sure to the card isn't being used for any automatic, recurring charges).
the only thing it looks like they screwed up on is that it sounds like that last statement never made it to you in the mail. you would have a hard time proving this, but if they're acknowledging that they "lost your address", then you should be able to convince them to let you just pay off the interest and they should waive the late fees.
incidently, as a practical matter, big banks maintain many different databases and as a result can have slightly different names and addresses for the same account. so the actual account database and the marketing database and the collections database might have different information. it shouldn't be that way, but in practice these things get out of sync all the time. that might explain how you never got statements but a collections notice found you.
in any event, good luck negotiating with them.
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