Why Mary Would Have Been Stoned To Death Without Joseph
The Jewish province of Judea in Ancient Rome was an exceptionally conservative, religious place. As Primo Levi Center says, Roman officials more or less let Pre-Christian Jewish people govern themselves, under their own laws, and only intervened in the case of "disturbances" (such as when Herod ordered the deaths of all first-born males, in order to kill Jesus). Gender roles were strictly defined, as were expectations when it came to sex and marriage. Deuteronomy 22:21, as a part of traditional Jewish law, pronounced a brutal and strict punishment for women who fornicated (no mention of punishment for the man), saying they were to be "... Brought to the door of her father's house and there the men of her town shall stone her to death. She has done an outrageous thing in Israel by being promiscuous while still in her father's house. You must purge the evil from among you."
So, it makes sense why a teenage, Jewish Mary (the eventual mother of Jesus) who visited her cousin and husband-to-be Joseph for several months, and then became pregnant, would have not been merely in a lot of trouble with society, but facing death as a result of her supposed indiscretion. It also makes sense that if Joseph wasn't the father, he would have wanted to dust off his hands and say bye-bye to his bride-to-be. That is, unless Joseph turned out to be precisely the kind of understanding, stand-up guy that he needed him to be.
Joseph didn't expose Mary to public shame
As Biblical Archaeology states, the Bible uses the Greek word mnēsteuō (pledged to be married) to describe Mary and Joseph's relationship in the time leading up to the birth of Jesus. Something between engaged and married, similar to "betrothed," this meant that Mary had passed along to Joseph's rule from her father's, but they were not yet allowed to have a sexual relationship. So, if Joseph noticed she was pregnant, whether he was the father or not, he could have exposed her and had her executed, even if only because he didn't want to bear the shame of being implicated in a pre-wedlock pregnancy. Before they were betrothed, this right would have fallen to Mary's father.
Overall, the Bible doesn't have much to say about Joseph, but his response to Mary's unexpected pregnancy might be all we need to know about him and his character. Joseph didn't rat Mary out, and in fact kept things hush-hush, no matter that he, as Matthew 1:19 says, "had in mind to divorce her quietly." At this point Joseph hadn't yet come around to accepting his divine fatherly duties, and it's understandable why he would have felt this way. Joseph also "did not want to expose her to public disgrace," which is a nice way of saying that he didn't want Mary murdered by rocks. Maybe not a high bar to clear in our eyes, but it was still exceptional for the time.
Joseph gets an angelic visit
Before Joseph could leave Mary, however, the Bible states in Matthew 1:20-25 that an angel appeared to him, saying, "... Do not be afraid to take Mary home as your wife, because what is conceived in her is from the Holy Spirit. She will give birth to a son, and you are to give him the name Jesus, because he will save his people from their sins." The passage goes on to say that this occurred as prophecy foretold. This heavenly intercession, similar to Mary's visit by Gabriel recounted in Luke 1:26-38, was all it took to make Joseph a believer, as the Bible says he was a God-fearing guy who, we presume, must have been acquainted with the prophecy.
The next morning, Joseph simply "woke up, he did what the angel of the Lord had commanded him and took Mary home as his wife." Easy-peasy. And just to be extra clear about the whole premarital sex issue, the passage in question goes on to say that Mary and Joseph didn't have intercourse before they were officially, formally married. In the end, it seems that the Almighty did a good job of choosing a couple to act as wards for His earthly incarnation.
Joseph stuck to his husbandly duties
All of this would have happened when Mary and Joseph were, as stated before, teenagers (Mary 13-16 or so, Joseph 17-19, per a Biblical discussion on Quora). We know this because only legal adults of ages 18 or higher were required to take part in censuses to pay taxes, which is why Mary and Joseph traveled to Bethlehem around the time of Jesus' birth. And as the Bible goes on to say, this is around the time when Emperor Augustus called for the aforementioned census, which more or less forced Mary and Joseph to stick together and not backpedal from their celestial commitment.
It would have certainly been a scandalous affair for a young, pregnant, betrothed couple to take to the road in those days, but Mary and Joseph did it, nonetheless. Mary accepted her role, and Joseph stuck by her side, claiming Jesus as his own child. They set off towards Bethlehem, and the rest of the well-known story unfolds: no room at the inn, settle into a nice nativity scene, get a visit from three wise men, and chill with some livestock. Despite a challenging, mystical start, Mary and Joseph stayed together, raising Jesus prior to him setting off to preach at age 30.