"The old woman is not getting off the airplane."
Translation:Az idős nő nem száll le a repülőgépről.
As I learned the other day (I'm not a Hungarian speaker, so take with a grain of salt) when you negate a verb like this, the prefix is separated from the verb and moves to the end.
If the sentence continued, I believe you can keep it together. For example: A nő nem leszáll a repülőgépről, hanem elalszik. Here there is more emphasis on what she did and did not do so the verb and prefix does not split. When there is no such emphasis, I believe you have to split it.