Obadiah says “the exiles of this host of the people of Israel” will possess territory as far as Zarephath (Obadiah 1:20). He also says “the exiles of Jerusalem who are in Sepharad shall possess the cities of the Negeb” (Obadiah 1:20).
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 1:20, then read the surrounding section so the answer stays connected to the passage's flow.
20The captives of this host of the children of Israel, who are among the Canaanites, will possess even to Zarephath; and the captives of Jerusalem, who are in Sepharad, will possess the cities of the Negev.