Appart from the various game options (OCC, no city razing, max city elimination(?)) which trigger/prevent the auto-razing of a size 1 city, there is only the 1 rule implemented that ParadigmShifter mentioned -- if a city has never had a population of 2 at any time in the game it will get auto-razed!
It is irrelevant how old the city is and how much culture it has produced. It is even possible for you to auto-raze a city which used to belong to you (but of course the only way this city could have changed hands before is via gifting/negotiating)
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