After a major environmental change, what happens to species that do not adapt or move?

There is great possible variations in the DNA of any species. However the possible variations are not infinite as postulated by Charles Darwin.

If there is a variation of the DNA of the species that is better adapted to the new environmental conditions than other variations or the original population this variation will survive and become the new dominate population.

A classic example of this is the Peppered moths of England. Before the Industrial revolution the typical peppered moth was white with dark spots. There was an existing variation called the melanic peppered moth that was mainly black.

During the industrial revolution large amounts of coal dust settled on the forest of England. This Environmental Change caused the typical white peppered moth to become nearly extinct in England and the Melanic peppered moth became the dominate species of peppered moths.

After the industrial revolution with less reliance on coal and better Environmental protection the tree became clean again. The cleaner trees was another Environmental Change. The dark colored melanic peppered moths again became a very small proportion of the peppered moths and the typical white moth again became the dominate species.

One concern presently is the Cheetah population in Africa. There is very little genetic variation in the Cheetah population. Most existing Cheetah are descended from a small breeding population. This leaves the Cheetah population very vulnerable to Environmental Changes.

After a significant environmental change, species that do not move or adapt run a greater risk of going extinct.