“On Mount Zion there shall be a remnant, and it shall be holy. The house of Yaakov shall dispossess those who dispossessed them.” (Obadiah 1:17)
Unlike the rest of the Temple, the Kotel Ma’aravi (the Western Wall) of the Temple Mount was built by King David, who prepared everything needed for the construction of the Temple (Sukah 53a). The Western Wall survived the destruction of both the First and Second Temples, and the Sh’khina (Divine Presence) has never left it (Shir HaShirim Rabba 2:9).
After the First Temple was destroyed, Ezra says, “Grace has been shown from Hashem our G-d to leave us a remnant and give us a peg in His holy place, so that our G-d may add luster to our eyes and give us a bit of sustenance in our bondage” (Ezra 9:8). The Western Wall was the “peg” to show us His intention to return.
And, indeed, it was rebuilt. Then, after the Second Temple was destroyed, the Western Wall was again left, as a sign for us that the Third Temple will be built. As our verse says, “On Mount Zion” — the Temple site — “there shall be a remnant” — the Western Wall — “and it shall be holy,” for the Divine Presence has ever left it, “and the house of Yaakov shall dispossess those who dispossessed them” with the building of the Third Temple.
Based on Birkat Hayyim, Haftarat Vayishlah, as cited in If I Forget Thee: The Ben Ish Hai on The land of Israel, Jerusalem and the Holy Temple