This is a misconception, migrating birds naturally overfeed before taking their long flights [1] and a few farms actually produce natural foie gras [2]. There was also a NYT article about a farm in Spain producing natural goose foie gras by trapping migrating geese. [ref needed]

Obviously this is totally marginal compared to the size of foie gras industry.

See

[1] https://honest-food.net/wild-foie-gras-is-real/

[2] https://www.theglobeandmail.com/life/food-and-wine/food-tren...

[3] https://modcarn.com/natural-foie-gras-in-the-wild/