How can one deal with a relationship between a young man and a young woman that involved foreplay, given the young man's desire to end the relationship out of fear of sin, and his apprehension due to the young woman's threats of suicide or abstaining from marriage? And would his leaving her be considered an injustice that prevents him from repenting?

What you have done is an abomination from two perspectives: establishing an emotional relationship with a foreign woman and engaging in unlawful touching, which is a type of zina (fornication/adultery). You must repent from this and be careful not to be lenient with foreign women. If the girl repents and you are destined to marry her, that would be good. However, if she declines marriage, you are not oppressing her. She should fear Allah and avoid suicide, and she can be cured of her infatuation by following the methods for its treatment.