Praise be to Allah.
What we think is that your suggesting her as a potential bride, when she is persisting in dressing immodestly, is not acceptable and in fact is not prescribed in Islamic teaching, because the one who is consulted is in a position of trust [and expected to give good, sincere advice]. The one who is asked to suggest a potential bride is being consulted by the one who asked him, and he is being asked to offer sincere advice. It is not sincere advice and it is not fulfilling the trust implied in being consulted to choose a woman who is like this to be a bride. Rather he should choose a woman who is religiously committed, of good character, and chaste and dignified; there are many such women, praise be to Allah.
Indeed, that is not appropriate. Rather that [suggesting her as a potential bride] should only happen after she has become religiously committed and started to dress modestly. The fact that people have rejected her and shown no interest in her, because of the way she is, is the right thing to do.
The first approach that you have adopted, which is telling her that people have rejected her every time you suggested her as a potential bride, is a good idea, to encourage her to wear hijab. If a woman sees that people are showing no interest in her because of her shameful behaviour, perhaps that will motivate her to check herself and rectify her condition.
With regard to the other approach, which is sending someone to try to chat her up in the street, and if she reacts to say to her, “You are the one who is encouraging people to chat you up and harass you because of the immodest clothes that you are wearing and because of your deviant behavior,” is something that it is not permissible to do, for the following reasons:
It is contrary to the general meaning of the verse in which Allah, may He be exalted, says (interpretation of the meaning): “Invite to the way of your Lord with wisdom and good instruction, and argue with them in a way that is best” [an-Nahl 16:125]. This approach does not come under the heading of wisdom, good instruction and arguing with them in a way that is best; rather it is the approach of evildoers and promiscuous people, because it is using shameful and hurtful words and phrases.
It exposes the one who is uses this approach to harm and problems with the family of this girl, and perhaps also with passers-by. This is not enjoined by Islamic teachings; rather it is forbidden.
It exposes the one who does that to insults and curses from the girl herself, and she may even report him to the police.
It comes under the heading of evil deeds that should be forbidden, so using it to forbid or stop another evil deed is futile. One evil deed cannot be stopped or changed by another evil deed.
In fact there is no guarantee that the one who does that to her will be safe from actually being tempted by her. How many people have opened the door to temptation, out of curiosity or just for fun, or thinking that they can set things straight, but soon fell prey to temptation and were overwhelmed, to the extent that no exhortation or rebuke could benefit them after that.
Rather what is required is for young women like her, who are pious and have knowledge of their religion, to exhort her wisely and gently. They should be patient with her and be friendly towards her, showing her love and sincerity, and letting her know that what is motivating them to advise her is simply their love of good for her and their keenness that she follow the straight path, so as to protect her religious commitment and her honour, lest those who follow their whims and desires get their hopes up. Then they should explain to her that she should follow the example of righteous and pious people, not evildoers and corrupt people, for the one who imitates a people is one of them, and the one who loves a people will be gathered with them (on the Day of Resurrection).
It is not valid for her to say, “I am not the only one who is doing this.” This argument is invalid both according to Islamic teachings and reason. Otherwise it would be permissible for everyone to do whatever he wanted, on the grounds that he is not the only one who is doing that; rather many people are also doing it. Allah, may He be exalted, says (interpretation of the meaning): “And if you obey most of those upon the earth, they will mislead you from the way of Allah” [al-An‘aam 6:116].
You could give her some Islamic booklets and tapes that speak about the hijab and dignity, and explain the negative effects in this world and the hereafter of immodesty and not adhering to the rulings of Islam.
Then after that, Allah guides whomever He wills and leaves astray whomever He wills, so whether or not she is guided is not up to you. Allah, may He be exalted, says (interpretation of the meaning): “Indeed, [O Muhammad], you do not guide whom you like, but Allah guides whom He wills. And He is most knowing of the [rightly] guided” [al-Qasas 28:56].
For more information, please see the answers to questions no. 88086 and 107783.
If you find that she does not respond to any of that, then it is prescribed to shun her by way of rebuking her for her ways, for when she sees the closest of people to her avoiding her because of the way she is, she will be humbled by it, and there is the hope that she will mend her ways because of that.
If she is so immodest that people point at her and she has become infamous for that, then it is even more important to shun her and keep away from her, so that the reputations of those who keep company with her will not be harmed.
See also the answer to question no. 114787.
And Allah knows best.