Is it permissible for my sister to work in a supermarket where pork is sold, knowing that she is a student and needs money, cannot find another permissible job, and my mother fears idleness for her?

Residing in disbelieving lands is impermissible except out of necessity or urgent need. A girl's study in schools in disbelieving lands is not free from falling into forbidden acts, such as impermissible mixing. A woman's work is not permissible unless it is regulated by Sharia guidelines, and work in a supermarket often lacks these guidelines. If the work involves selling forbidden items, then it is impermissible. It is preferable and safer to leave it, just as a woman's work in this field cannot be regulated by Sharia guidelines. It is advised to leave those lands and strive to reside and seek a livelihood in an Islamic country. If that is not possible, then one must be mindful and preserve one's religion.