Load a credit card with that amount of funds necessary. Or even better, give her the number of a credit card in your name with a low limit (something like 5000$), enough to get out in a pinch. Most people when buying a plane ticket buy them on-line anyway and you need a credit card.
Or, alternatively, set up a separate credit line to your account with the funds. If your family member needs to get out, you release the information and she can buy her plane ticket.
If she doesn't need the money, you can still reclaim it because she hasn't spent it.
Best of luck to your family