What is the ruling of Islamic law on preventing an unmarried sister from traveling to a medical conference and staying overnight 100 kilometers away for two days, knowing that the father has passed away?

A woman is not permitted to travel without a mahram, based on the Prophet Muhammad's (peace be upon him) saying: "A woman must not travel except with a mahram." However, there is no objection to her residing away from home without a mahram, provided she is safe and free from religious transgressions. If your sister wishes to travel with a mahram to reside in a city for two days, and her stay is safe, then there is no impediment. But if her stay is not safe, or if she intends to travel without a mahram, then you must convince her to reconsider. It is also advisable to seek a righteous husband for your sister.