She must have been given an earful by another foreigner, so now she keeps the racket to Taiwanese only.
A few days ago there was a report of a very successful scam. This guy at foreign airports, like Bangkok or Osaka, approaches the Taiwanese passengers. He tells them his bag was stolen, can they lend him some money? He shows a plane ticket headed to Taiwan.
All Taiwanese interviewed said they would easily give him 4000 or 5000 NTD, as he is a fellow Taiwanese in trouble.
There are more than 20 reports of his victims this month alone.
Begging for money for a flight ticket back home or otherwise shouldn’t be allowed as it implies you broke the law.
Entering Taiwan on a tourist visa without a return ticket is not allowed. Usually the airlines are enforcing those rules when you check in to your flight to Taiwan. Border agents also might ask to see the return ticket (usually they don’t). You can simply circumvent it by buying a return ticket that is 100% refundable for a short period of time and refund it after you enter the country.
I would call the police. People who are in this situation are supposed to contact their country’s representative office for assistance instead of begging on the streets.