Nidhogg is best understood as one position in a system rather than as a character. Yggdrasil has a creature at every level: an eagle at the crown, four harts browsing the branches, goats and serpents, and the dragon below gnawing at the root. The squirrel Ratatoskr runs the length of the trunk carrying insults between the eagle and the dragon, which is the only piece of Norse cosmology that is straightforwardly funny.
What the arrangement describes is a tree under constant attack that goes on standing. Nothing in the sources suggests the gnawing will succeed. The tree suffers more than people know, one poem says, and that is the whole claim: the structure of the world is maintained against continuous damage rather than being permanent by nature.
The dragon's other post is Nastrond, the shore of corpses, where it feeds on the bodies of oath-breakers and murderers. The last stanza of the great prophetic poem has Nidhogg flying up over the plain with corpses in its wings, and editors have argued about that stanza for a long time, since a poem describing the world renewed after the end appears to close with the old horror still in the air. Some read it as the final note of an unresolved ending; others suspect it has been moved. The manuscript gives no help.