Every time you enter a country, you go through passport control and they stamp your passport on the blank pages at the back. People tear out pages, if they don’t know how risky it is, in order to conceal their previous movements. If you get caught doing that, as she found out, you get stuck where you are. That airport person was on the ball.
You have to have a minimum of so many blank pages, usually three, in you passport to obtain permission to enter most countries. If you use your passport a lot you can run out of space quite easily. You then have to go to an American Embassy or Consulate overseas, or the Post Office stateside, get get more blank pages inserted into your passport. She obviously did not know this and found out the hard way.