Ever heard of a "tree surgeon"? They manipulate stems, twigs and roots, sometimes cutting the sick branches, sometimes putting healthy branches back into other plants for both cosmetic and health reasons (of the plant in question).
Here at the office we dubbed the results "Frankentrees", so of course I had to google it.
I've heard of people who do this with fruit trees, ie. getting a branch of a plum tree to graft onto another kind of fruit tree,, and continue to produce fruit.