To escape death, change your shape: the pattern here lets the doomed slip the killing blow by becoming something else. Our clearest witness is Greek, and it is the gods themselves who run.
Apollodorus's Library (Bibliotheca) (a Greek mythography of the 1st–2nd century CE) tells of Typhon, the monster Earth bore against heaven — a thing so huge that "his head" "often brushed the stars", "spouting a great jet of fire from his" mouth. "But when the gods saw him rushing at" heaven, "they made for Egypt in flight," and, pursued, "changed their forms into those of" beasts. Divinity does not stand and die; it turns animal and hides. James George Frazer (1854–1941), the Scottish classicist who Englished this Library and wrote The Golden Bough, notes drily that the tale "was probably invented by the" Greeks "to explain the Egyptian worship of animals" — a story grown up to account for the beast-headed gods along the Nile. Whatever its root, the deed is bare escape: the shape is shed to save the life.
A second, looser witness sits on the shelf in Myths & Legends of China (a compilation published 1922), where the demigods of a battle of the gods are "gifted with marvellous powers" and "could at will" "change their form". But there the shifting is mostly a weapon or a capture — a beaten Immortal forced to "reassume his original form" as a peacock or a turtle — not the panic flight of the Greek gods, and it strains to answer the motif's own name.
Only these two are wired to served text; Thompson's Icelandic, Jewish, Indian, Toba, Aztec, Greenland and Ekoi authorities all wait unread. When even gods must turn into beasts to live, is transformation a power here, or a confession of fear?