Praise be to Allah.
A woman should choose a righteous man for her husband; it is not permissible for a guardian to reject a man who is religiously committed and of good character, if he comes seeking marriage to a female relative under his care.
A man must also make a good choice of a wife. The Prophet (peace and blessings of Allaah be upon him) advised men to marry women who are religiously committed, for a righteous woman will protect a man’s house, wealth and children.
Engagement is no more than a promise to marry. The fiancé is still a non-mahram to his fiancée and it is not permissible for him to be alone with her, shake hands with her or go out with her.
This young woman and this young man have to repent to Allaah for the sins that they have committed. What happened is not surprising, because both of them got engaged without adhering to the Islamic rulings.
With regard to her canceling the engagement, it says in Fataawa al-Lajnah al-Daa’imah (18/69): An engagement between a man and woman is not equivalent to a marriage contract. Either the man or the woman may cancel the engagement if they think it is better to do so, whether the other party agrees or not.
The sister should note the danger of corresponding and conversing with the opposite sex, because this may lead to many negative consequences. The internet is full of stories of women who were careless about such matters to the extent that they lost their honour, and women who did such things because they thought it was just for fun or that they would be able to protect themselves, but they quickly fell into the wolf’s lair.
And Allaah knows best.