Where is the Scripture that talks about living together if unmarried?
Generally the phrase "living together" is a polite way of saying that two people are sharing the same bed in the same home, thus engaged in sex, though unmarried. In the Greek, the word for this is pornos, which means engaging in sex outside of marriage. In many of the more literal translations, this word is rendered as "fornicators." Unfortunately, many of the newer translations have decided that fornication is too archaic of a word and so they have tried to modernize the term with either "sexually immoral" or "immoral." I say unfortunately because these phrases are so vague -- especially "immoral" -- that readers miss the meaning entirely.
Occasionally I run into some who claim that they only plan to share an apartment or home. Though they are not of the same sex, they have no intention of engaging in sex. They are just splitting the cost of maintaining a place to live. I suspect that 99% of these people are not being fully honest about the situation. While they might not intend for things to go that far, it is difficult to maintain a distance when you are living closely together.
However, let us just suppose that two unmarried, unrelated people were able to live in the same home without engaging in sex, would it be proper? We have to think about not only what is actually happening, but we must also consider the message we are sending to other people by our actions.
For example, Paul was once gathering funds to relieve famine victims in the Judea area. Though he was an apostle of Christ and had no intentions of putting his hand in the till, he asked the churches sending the money to select men to carry the money. "And when I come, whomever you approve by your letters I will send to bear your gift to Jerusalem. But if it is fitting that I go also, they will go with me" (I Corinthians 16:3-4). Didn't people trust Paul? Of course, they did! Then why the extra people? "And we have sent with him the brother whose praise is in the gospel throughout all the churches, and not only that, but who was also chosen by the churches to travel with us with this gift, which is administered by us to the glory of the Lord Himself and to show your ready mind, avoiding this: that anyone should blame us in this lavish gift which is administered by us -- providing honorable things, not only in the sight of the Lord, but also in the sight of men" (II Corinthians 8:18-21). Paul knew he was honest. The brethren knew he was honest. But Paul didn't want anyone to ever doubt his honesty or to have an occasion to claim that something might have happened.
The same concept needs to be considered in living arrangements. If a man and woman are living in the same home or apartment, what are people going to assume? Given the high prevalence of people having sex outside of marriage, their assumption is probably right the vast majority of the time. Why give people a false impression? Why cause people to assume that you, as a Christian, are breaking God's law? So, even here it is not proper for two unmarried, unrelated people to share the same home.