Is it permissible for a woman to travel without a mahram to work in another country if her psychological and financial condition is poor, and are there any exceptions to this ruling?

Your sister's delayed marriage is a matter of divine decree and destiny. You should pray and maintain a good opinion of Allah. Regarding her travel for work: a mahram (unmarriageable kin) is required for travel, not for residence. If she cannot find a mahram, her travel by plane may be permissible if she is not exposed to temptation, due to the prevalence of security in such journeys. Some scholars, such as Al-Hattab Al-Ru'ayni, Al-Baji, and Al-Zanati, have permitted a woman's travel without a mahram in large caravans, secure companies, and armies, considering there to be no difference between this and remaining in one's town. Sheikh Ibn Jibreen also holds that the prohibited journey is one that takes a day and a night, whereas short, safe journeys are not included in the prohibition.