Obadiah says the house of Jacob will consume the house of Esau, and “there shall be no survivor for the house of Esau” (Obadiah 1:18). He presents this as the LORD’s declared outcome: “for the LORD has spoken” (Obadiah 1:18).
Obadiah closes by turning from Edom’s downfall to Zion’s future. On Mount Zion there will be survivors, the place will again be treated as set apart, and Jacob’s family will regain what was taken. Israel is pictured as fire consuming Esau like dry straw until none remain. This unit concludes the book’s movement from announcing Edom’s coming humiliation (earlier in the oracle) to explaining why Edom is singled out for violence against Judah, and then to the wider horizon of “the day” when outcomes reverse.
Obadiah ends by reversing the earlier picture of Judah’s disaster and Edom’s advantage. The text explicitly says that survivors will be on Mount Zion, Zion will be treated as set apart, and Jacob’s family will regain what is theirs (verse 17).
A careful answer keeps the immediate passage, the book's argument, and the whole-Bible storyline together, so the question is answered in context instead of as a detached idea.
Start with Obadiah 1:18, then read the surrounding section so the answer stays connected to the passage's flow.
18The house of Jacob will be a fire, the house of Joseph a flame, and the house of Esau for stubble. They will burn among them, and devour them. There will not be any remaining to the house of Esau." Indeed, Yahweh has spoken.