Commentaire sur Les Nombres 24:18

והיה ירשה שעיר איביו SEIR ALSO SHALL BE A POSSESSION [FOR HIS ENEMIES] — for his enemy, Israel.

AND EDOM SHALL BE A POSSESSION, SEIR ALSO, EVEN HIS ENEMIES SHALL BE A POSSESSION. The downfall of Edom²⁵⁰See Vol. I, pp. 444-445, and 568-569, for an explanation why this term is used about Rome. will be by the hand of the Messiah, because our present exile under the hand of Rome is considered Edom’s [exile], just as it is said: The punishment of thine iniquity is absolved, O daughter of Zion, He will no more carry thee away into captivity; He will punish thine iniquity, O ‘daughter of Edom,’ He will uncover thy sins²⁵¹Lamentations 4:22. — for G-d will not punish Edom until the sins of Zion are absolved, at the time when He will no more keep them in captivity.²⁵¹Lamentations 4:22. Therefore Balaam mentioned Edom, for it is he who disputes our [right to] kingdom, and about him it has been said, and the one people shall be stronger than the other.²⁵²Genesis 25:23. “They will never be equally great at the same time; when one rises, the other will fall” (Rashi ibid.). Balaam was thus prophesying that Edom will not completely fall until the time of the end [of the exile] by the hand of ‘the star’ [i.e., the Messiah] who will step forth out of Jacob [as stated in the previous verse].
Seir also, even his enemies shall be a possession. This means that Seir will become a possession of his enemies [i.e., of Israel].²⁵³This is Rashi’s interpretation, according to which the phrase his enemies is to be interpreted as to his enemies. Or [the term] his enemies may refer to [Jacob’s enemies, i.e.,] Edom and Seir mentioned [previously in the verse], who are the enemies of Jacob, [and the meaning of the verse would thus be: “Edom, and Seir also, who are the enemies of Israel] will become a possession [of Israel].”²⁵⁴See my Hebrew commentary p. 301 for a quote from the Zohar, which interprets the verse in this way.

שעיר איביו, "even Se-ir his enemies." Bileam lumps Edom and Se-ir together as being one. The word ירשה implies that that which has been destroyed will not be rebuilt. Edom will not rise again from its ruins as will other nations. The reason is that these people were enemies of Israel, איביו. Compare Psalms 137,7 where the Jewish people are quoted as asking G'd to pay back the people of Edom for what they have done to them. The Psalmist pleads with G'd to destroy Edom to its very foundations. This is why Bileam predicts that Edom's defeat will be much more severe than that of the other descendants of Sheth.