Your parents love your sister, and they know she's heading down a road that could bring her great unhappiness and they don't want that to happen. They also know that what she's doing is wrong in God's eyes; they may feel hurt too because she is rejecting all they tried to teach her.
But I hope your parents will look beyond their immediate hurt and try to keep the door open. After all, this type of arrangement is always insecure and shaky and the reason is because there is no lasting commitment. Marriage involves a commitment of a man and woman to each other but simply living together lacks that commitment.
The time may well come, therefore, when your sister will find herself rejected and if so, she will need the love of her family. The father of the prodigal son had every reason to be upset at his son's sinful lifestyle. But when the son realized the error of his ways and returned home, we read that the father "was filled with compassion for him; he ran to his son, threw his arms around him and kissed him" (Luke 15:20).
This is a vivid image of how God treats us when we repent and come to Christ but it also gives us a pattern to follow. Pray for your sister, and pray also for your parents. This is a difficult time for them, but God can use you to encourage them.