In the story of Ragnarok, Lif and Lifthrasir survive by hiding in Yggdrasil, and presumably they go on to repopulate the world after all the fighting is over.
Are there any other cultures whose end-of-the-world myths explicitly include some survivors who could potentially rebuild civilization?
Yes. Many different cultures and mythologies depict really similar stories about floods. There are only a handful survivors of the flooding, who have to repopulate the earth.
For the Sumerian version of the myth, Enlil sends a flood to kills the too-numerous and too-noisy humans. The god Enki intervenes and warns the king to save his family and a collection of animals. Babylonians have a similar version of the myth in which a man called Tnapishtim built a boat, took aboard his family and a selection of craftspeople and animals. The well-known Judeo-Christian version of the myth has Noah build an ark, take aboard seven family members and representatives of all land animals to survive a global flood. The list goes on.
In Greek mythology there is Deucalion and Pyrrha
In Greek mythology, Deucalion (Greek: Δευκαλίων) was the son of Prometheus; ancient sources name his mother as Clymene, Hesione, or Pronoia.1 The anger of Zeus was ignited by the hubris of the Pelasgians, so he decided to put an end to the Bronze Age. Lycaon, the king of Arcadia, had sacrificed a boy to Zeus, who was appalled by this savage offering. Zeus unleashed a deluge, so that the rivers ran in torrents and the sea flooded the coastal plain, engulfed the foothills with spray, and washed everything clean. Deucalion, with the aid of his father Prometheus, was saved from this deluge by building a chest.[2] Like the Biblical Noah and the Mesopotamian counterpart Utnapishtim, he uses his device to survive the deluge with his wife, Pyrrha.
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Once the deluge was over and the couple had given thanks to Zeus, Deucalion (said in several of the sources to have been aged 82 at the time) consulted an oracle of Themis about how to repopulate the earth. He was told to cover your head and throw the bones of your mother behind your shoulder. Deucalion and Pyrrha understood that "mother" is Gaia, the mother of all living things, and the "bones" to be rocks. They threw the rocks behind their shoulders and the stones formed people. Pyrrha's became women; Deucalion's became men.
Deucalion and Pyrrha had at least two children, Hellen and Protogenea, and possibly a third, Amphictyon (who is autochthonous in other traditions).
