Praise be to Allah.
There is nothing wrong with your sister working in the students’ residence, especially if it is in your city, but if it is in another city then it is not permissible for her to travel there and back except with a mahram, but it is permissible for her to stay in that residence without a mahram, because what is required is only that she be accompanied by the mahram on the road. The same also applies to the female students who live there. Your sister is not expected to examine each student to find out whether she came with her mahram or travelled without him, rather it is sufficient that her work in the residence does not involve anything haraam. Administration, guard duties, cleaning and so on are all permissible and there is nothing wrong with that, in sha Allaah.
Shaykh Ibn Baaz (may Allaah have mercy on him) said in Fataawa Noor ‘ala al-Darb (tape no. 288):
There is nothing wrong with what you have done. There is no harm in a woman staying or living in a city without a mahram and there is no sin in it, especially if there is no danger involved in that, if she is among other women or in a workplace that is separate from men doing work that Allaah has permitted, or in a department that is women-only. There is nothing wrong with any of that. What is forbidden is travelling; you should not travel except with a mahram, and you should not come without a mahram. As for staying among women doing permissible work, there is nothing wrong with that, praise be to Allaah. End quote.
See also the answer to question no. 45917.
With regard to the hadeeth mentioned at the end of the question, it is the hadeeth of ‘Aa’ishah according to which the Prophet (peace and blessings of Allaah be upon him) said: “There is no woman who takes off her clothes anywhere but in her own house, but she has torn (the veil) which exists between her and Allaah.” Narrated by Abu Dawood (4010) and classed as saheeh by al-Albaani.
Al-Manaawi said in Fayd al-Qadeer (3/163), commenting on this hadeeth:
It is a metaphor for her uncovering herself before non-mahrams and not covering herself in front of them. End quote.
What is meant in this hadeeth is a woman who takes off her clothes in the presence of non-mahram men, or in a place where non-mahram man can see her, such as public places or places frequented by evil-doers and the like. But if she is in a safe place, such as if she is in the house of her mahrams or parents, or in a place where she and her husband have made a stop during a journey, or she needs medical treatment or she needs to do ghusl for some shar’i reason and so on, then there is no sin on her, and the hadeeth does not forbid such cases.
This has also been explained in the answer to question no. 34750.
The sincere Muslim carries his da’wah with him wherever he goes. If the situation in the students’ residence is as you describe, and there is little righteousness, then your sister should strive to spread goodness there and enjoin what is good and forbid what is evil, and strive to change things for the better as much as she can. Thus she will fulfil her duty before Allaah.
Shaykh Ibn Baaz (may Allaah have mercy on him) was asked the following question in Majmoo’ al-Fataawa (7/274):
I am a girl who lives in the students’ residence. Allaah has guided me to the truth, and I have begun to adhere to it, praise be to Allaah. But I am very upset because of what I see around me of some sins and evil deeds, especially among some of my fellow-students, such as listening to music and malicious gossip. I advised them often but some of them make fun of me and mock me, and say that I am being extreme. What should I do, may Allaah reward you with good?
He (may Allaah have mercy on him) replied:
What you have to do is denounce the evil as much as you can, by kind words and good manners, quoting verses and ahaadeeth which speak of that, according to your level of knowledge. Do not take part in listening to music or gossiping or other haraam words and deeds, and withdraw as much as you can until they start to speak about something else, because Allaah says (interpretation of the meaning):
“And when you (Muhammad) see those who engage in a false conversation about Our Verses (of the Qur’aan) by mocking at them, stay away from them till they turn to another topic”
If you denounce them as much as you can and withdraw from what they are doing, then their deeds or criticism of you will not affect you, as Allaah says (interpretation of the meaning):
“O you who believe! Take care of your ownselves. If you follow the (right) guidance [and enjoin what is right (Islamic Monotheism and all that Islam orders one to do) and forbid what is wrong (polytheism, disbelief and all that Islam has forbidden)] no hurt can come to you from those who are in error. The return of you all is to Allaah, then He will inform you about (all) that which you used to do”
Allaah explains that the believer will not be harmed by those who go astray if he adheres to the truth and follows true guidance, by denouncing evil and adhering steadfastly to the truth and calling others to it. Allaah will grant you a way out, and Allaah will benefit them by means of your guidance if you are patient and seek reward, in sha Allaah. Receive the glad tidings of great goodness and good consequences so long as you remain steadfast in adhering to the truth and denouncing that which goes against it, as Allaah says (interpretation of the meaning):
“and the (blessed) end is for the Muttaqoon (the pious)”
“So be patient. Surely, the (good) end is for the Muttaqoon (the pious)”
“As for those who strive hard in Us (Our Cause), We will surely guide them to Our paths (i.e. Allaah’s religion — Islamic Monotheism). And verily, Allaah is with the Muhsinoon (good-doers)”
May Allaah help you to do that which pleases Him and bless you with patience and steadfastness, and may He help your sisters and family and colleagues to do that which He loves and which pleases Him, for He is All-Hearing, Ever-Near, and He is the Guide to the straight path. End quote.
And Allaah knows best.