Salamualaikum. Let me first clear the air by saying I'm in no way shape or form supporting rape, but all I want is clarification. My question is if an inappropriately dressed woman goes out late in the night for no reasonable purpose and gets raped, doesn't she share a part of the blame, however small, for tempting the rapist? Remember, not only did she dress inappropriately, she also went out late in the night for no good reason. This question is as a result of the fact that many women even Muslim women want to hide under the cover of "the victim is never at fault" and dress inappropriately. I'm not even in support of this mantra because in some cases I believe the victim takes a part of the blame. I know Islam doesn't support rape but it also frowns at indecent dressing from both men and women!
And no bearer of burdens will bear the burden of another. And if a heavily laden soul calls [another] to [carry some of] its load, nothing of it will be carried, even if he should be a close relative. You can only warn those who fear their Lord unseen and have established prayer. And whoever purifies himself only purifies himself for [the benefit of] his soul. And to Allah is the [final] destination.
— Faatir 18]
There really is no such thing as "distribution of blame" in Islam: The woman is responsible for her own actions and accountable for her own sins, and the rapist is responsible for their own actions and accountable for their own sins. The issues can't be conflated as you're doing here, they need to be judged separately.
In other words, whatever sin the woman committed by dressing indecently in no way lessens the burden of the sin on the rapist, or vice-versa: They are both still fully accountable for their own actions.
I think that you may not be educated on Islam. There is no ruling preventing women from going out at night even without a valid "reason". There is a hadith regarding a woman who went out late at night and got raped. Abu Alqama reported: A woman went out to pray during the time of the Prophet, peace and blessings be upon him, and she was met by a man who attacked her and raped her. She screamed and he ran away. Then another man passed by and she said, “This man has molested me!” A group of emigrants were passing by and again she said, “This man has molested me!” They caught the man whom she thought was her attacker and brought him to her and she said, “Yes, this is the one.” They brought him to the Prophet and he issued orders concerning him but the one who had attacked her stood up and he said, “O Messenger of Allah, I am the one who attacked her.” The Prophet said to her, “Go now, for Allah has forgiven you,” and the Prophet said kind words to the man who had been mistakenly arrested. The Prophet said to the man who had attacked her, “Stone him,” and the Prophet said, “Verily, he has repented in such a manner that if the people of Medina were to repent in this way, it would be accepted from them.”
Source: Sunan al-Tirmidhī 1454