Yes, the roots cannot grow once the stump is removed because roots need nutrients to grow that can only be supplied by the tree’s leaves.

Without the leaves, the roots die. It’s the leaves that supply the necessary fuel obtained by photosynthesis.

Any stump left in the ground can reshoot after it’s been cut down. It’s important to realize that any new growth will provide fuel to the root system. You should have any new sprouts removed as soon as they begin to grow.

The shoots should be removed by cutting them and a small piece of the root to which they are attached, this can be done using garden tools or with the use of herbicides.