I've caught feral cats before by getting them used to eating inside a crate. And then one day closing the door while they are eating.
You might have to start by putting the food at the opening of the crate. Then a couple inches in. Then halfway in. Then at the back.
Good job saving this kitty. <3
Also it is completely incorrect that cats have to be hungry to hunt. The truth is malnourished cats are less effective hunters. If your parents want a barn cat for rodent control there may be a program in your area. The cat would be vaccinated and nuetered. They would be responsible for providing shelter and daily food.