Let us look at this passage again:
"And it shall come to pass, that in all the land, saith the LORD, two parts therein shall be cut off and die; but the third shall be left therein. And I will bring the third part through the fire, and will refine them as silver is refined, and will try them as gold is tried: they shall call on my name, and I will hear them: I will say, It is my people: and they shall say, The LORD is my God" (Zech.13:8-9).
According to what is said in "bold" we can understand that the third which will remain will be saved. Besides that, let us look at this passage:
"Behold, the days come, saith the LORD, that I will make a new covenant with the house of Israel, and with the house of Judah: Not according to the covenant that I made with their fathers in the day that I took them by the hand to bring them out of the land of Egypt; which my covenant they brake, although I was an husband unto them, saith the LORD: But this shall be the covenant that I will make with the house of Israel; After those days, saith the LORD, I will put my law in their inward parts, and write it in their hearts; and will be their God, and they shall be my people. And they shall teach no more every man his neighbour, and every man his brother, saying, Know the LORD: for they shall all know me, from the least of them unto the greatest of them, saith the LORD: for I will forgive their iniquity, and I will remember their sin no more" (Jer.31:31-34).
First, we can understand that the "fathers" of those from the houses of Israel and Judah were the ones who broke the covenant and those "fathers" were the physical descendants of Abraham, Isaac and Jacob. Therefore, they are also physical descendants of the same men.
And all of them will know the Lord and all of them will have their sins forgiven and thus be saved.