This is a very different condition than I described in Toba Hawthorn, Pruning a Tangle. This is man-made, usually out of ignorance, and is a serious attack on its system. Thankfully less common than it used to be, it is still out there. It is a lack of thinking and knowledge, knowledge that I speak of in Botany 1, the Whole Tree.
What happens is that a decision to shorten, to top the Tree at a certain height is made. The lower you go, the more leaf mass you remove. On crab apples, if you go low enough, so that your cuts are 3 inches in diameter, you will effectively have removed most of the leaf-bearing branches. You will have removed most of the leaves. For a being that feeds itself with its leaves, this is an emergency. The Tree's reaction will be immediate, to grow as many new shoots as possible to replace the lost leaf mass. The other major damage is inside the trunks, unseen; a large percentage of healthy trunk tissue has been used up to defend the Tree's inner system from the air.
See An Arborist Thinks on Compartmentalization.
In the year following this attack, the cut ends of the trunks will begin to look like brooms, with dozens of new shoots working hard to feed the starving Tree. The best thing is to leave it alone for a few years. This will do two things: allow the Tree to stabilize after the emergency and allow the dominant shoots to assert themselves. Once the Tree has recovered and is showing major dominant shoot growth, we could now think of pruning, thinning the tangle.
I use a system where I keep as many of the dominant shoots as possible. Most times this requires selecting the strongest two or three and removing the others. I also thin most of the little guys, especially those who grow back into the Tree or into other sections of the Tree. When this thinning work is completed the Tree won't look much different from before the initial hard pruning, with one huge exception; its life span has been reduced, due to the loss of healthy interior trunk space. Fortunately this situation is in decline. As people educate themselves more about Trees, and wives take away dangerous toys from their husbands, Trees will be allowed to flourish.