In the future, the nations will be destroyed which is symbolized by the big animals being cut, while the Jews live eternally, which is symbolized by the birds staying whole. This is written in the second Rashi in Genesis 15:10.
"but he did not divide the birds: Since the idol-worshipping nations are likened to bulls, rams, and goats, as it is said (Ps. 22:13): “Many bulls surrounded me, etc.,” and Scripture states (Dan. 8:20): “The ram that you saw, the one with horns, represents the kings of Media and Persia,” and Scripture states (ibid. verse 21): “And the he-goat is the king of Greece.” And the Israelites are likened to young doves, as it is said (Song of Songs 2:14): “My dove, in the clefts of the rock.” Therefore, he divided the animals, as an allusion that the nations will gradually perish. “But he did not divide the bird,” as an allusion that Israel will exist forever. [from Pirkei d’Rabbi Eliezer , ch. 28; Targum. Ps. 22: 13]"