I had a pecan tree, which was more than 20 years old. I cut it down because the trunk near the ground was partially rotted and the tree did not look healthy, though not dead. Now a new tree (about 3 feet tall now) is growing out of the old root and it looks healthy. I would love to keep it as long as it is going to be a healthy tree. Is it worth saving it?
Disease not withstanding and if nothing else is wrong the tree will grow, but it will never regain its former glory. Except for a select few species like locusts and aspens, trees that develop from suckers never do much of anything except annoy.