There still were some in the Third Age in the south of the Ered Luin and these were probably either descendants of those that never left the area or of those that fled after the awakening of Durin's Bane.
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and then the glory of Moria passed, and its people were destroyed or fled far away.
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went into the far North to the Grey Mountains, where most of Durin's folk were now gathering
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Both from the Appendix.
So first it's said that the people of Khazad-dûm fled far away and then that Durin's folk was gathering in the north. So what about the others?
Maybe they decided to go back to their ancestral homes and split up with Durin's folk.
They clearly would have had contact to Thráin and so some went with him on the quest.