Well, they wouldn't have had far to go. And, nice as the Chaco cultural hearth may have been, when a drought hits, such as the 25-year dry spell from around 1280-1320 AD, people cannot sustain in place. They have to go near a river that gets snow runoff.
At about the same time, there were invaders from what is now Mexico (hmmm) and, being of Aztec persuasion, they were much more able to make war and intimidate (it is thought they also brought cannibalism, ritual or otherwise, to the region -- as butchered human bones should suggest).
The little Mogollon people in Eastern AZ and Western NM also vanished about this same time.
Interesting thing is that in the same time frame the cahokia pyramid people of southeastern Illinois also disappeared. Its thought that the climate change that brought drought to the south west also brought big flooding to the Mississippi valley for the first time 400 years.
Nobody likes to point this out because it isn't politically correct, but they also were not very good a managing their resources. They used a lot of wood, but never planted any trees to replace the ones they cut down. Kind of odd, since they were good farmers. After a few hundred years the trees were gone in the southwest, and the topsoil blown away. The land is still recovering.
Read Louis L’Amour’s novel, “Haunted Mesa”
The Anasazi mystery is the foundation of his story. And he’s a great American western author, so it’sa good read..