If a girl is having a relation with a boy secretly (as a bf and gf) and get caught by her family, then what should be her family's reaction towards her and if she realized her mistake and apologizes with her true heart? Please tell me about both of these situations According to Islamic point of view. Thank you
If we imagine this happening in a middle class Muslim family living in a Western country, then she is forgiven and life goes on like normal, regardless of whether the relationship involved sexual intimacy or not. Islamic law has nothing more to say on this situation beyond the fact that a family should not allow a daughter or son to have casual sexual relationships with others while living under the parents’ roof (it is part of the parents’ duty to prevent such a situation from coming about).
If they were living in an imaginary country where Islamic law is followed in a modern and civilized manner, then when she says she has had a relationship with a man, whether it involved sexual intimacy or not, then again she is forgiven and life goes on like normal, because in Imam Malik’s hadith collection al-Muwaṭṭaʾ the Prophet 
recommends that people involved with such sins should repent and keep it secret rather than publicizing their sin.1
The only case where should would suffer punishment is if she is living in that imaginary Islamic country and has sexual intimacy with a man in such a public manner that four people see it and go on to report it to the authorities. The Islamic laws punishing sexual misconduct are there to prevent this level of breakdown in sexual morality. In such a case her punishment would be public flogging.
It should be noted that in a modern and civilized Islamic state there would be a constitution that applies to everyone, Muslim and non-Muslim, and Islamic law would only apply to Muslims (as is the case in Malaysia). People should also have the right to leave Islam. In such a civilized Islamic state, Islamic law would only apply to people by their own choice, since they have the right to leave Islam. So the Islamic punishment of flogging would be the Muslim community’s internal business. An atheist who does not like this punishment would be free to leave Islam so that Islamic law no longer applies to them. I believe this way the Quranic ideal of not forcing religion on anyone can be achieved, while Islamic law can be followed by those who believe in it and appreciate its internal logic.
However, if were to talk about today’s actual Muslim societies, then the way such a situation is dealt changes greatly from place to place and from one class of society to another. The upper and middle class in most places would act the way I described (letting the matter go). But uneducated and lower class Muslims, who often know very little about Islam, judge things by their cultural norms (rather than religious beliefs), and such people may punish her severely, lock her up or in the worst cases kill her (an act that would be considered murder in a civilized Islamic state). While today it is highly fashionable to blame Islam for this type of killing (an “honor killing”), people who blame Islam for honor killings are merely showcasing their prejudice. Honor killings also happen among India’s Hindus and the Catholic Christians of India and Pakistan, for example. Until recently fathers and husbands in China had the right to kill daughters who were deemed to have dishonored the family.
An issue that complicates the matter is that many traditionalist Muslim scholars today continue to support the Jewish punishment, not found in the Quran, of stoning married adulterers who are caught by four witnesses during the act of copulation. Even though almost no living Muslim today has seen this punishment carried out against anyone (due to the extremely stringent evidence requirements, the fact that silence is encouraged, and the fact that most Muslim countries do not have a legal system that recognizes the punishment), theoretically it could be carried out in some imaginary Muslim land. The highly respected 20th century Egyptian scholar Muḥammad Abū Zahra rejected it based on a number of strong legal and historical arguments (I will write a separate article on his views one day inshaAllah), and the mainstream Islamic scholar Yusuf al-Qaradawi spoke of Abū Zahra’s opinion as a valid alternative opinion to the traditional one although he himself has not so far declared that he agrees with it personally.