Is it permissible to remain in university housing after discontinuing university studies, knowing that the housing is designated for students and its fees have been paid in advance?

The reference for entitlement to residence is the university's system and its conditions. If the system prohibits residence in the accommodation upon discontinuation of studies, then residence is not permissible, based on the Almighty's saying: "O you who have believed, fulfill [all] contracts," and the Prophet's (peace be upon him) saying: "Muslims are bound by their conditions, except a condition that makes a lawful thing unlawful or an unlawful thing lawful." As for a girl residing in a country other than her own without a mahram, it is not forbidden if she is safe. What is forbidden is a woman traveling without a mahram, according to the majority of scholars.