What is the ruling on a woman traveling for study and knowledge in an Arab country with a mahram who does not stay with her, but rather places her in a safe student dormitory due to the impossibility of him staying with her?

It is not a condition that the mahram reside with the woman in her country of residence if she is safe therein. Rather, the presence of a mahram is a condition during travel, as stated in the hadith: "A woman must not travel except with a mahram." Scholars have stipulated that the mahram who travels with a woman when she is exiled due to adultery may return once he is certain of her safety.