If dying is the process of proceeding towards death, then we are all - by definition - in the process of dying, at the very same time as we are living.
This is not a very satisfying perspective. Perhaps a better analogy to use would be a train traveling inexorably on a seemingly endless track. This track does end, however... at the edge of a cliff. What we traditionally call "living" is like being on that track headed towards the cliff. Then, what we traditionally call "dying" is actually launching off of the cliff and plumeting to the bottom, to be destroyed in the cataclysmic crash. But as long as you are still falling and haven't yet hit the ground, you are still alive. So, technically, if the train can't stop its engines - if we can't stop time - then the train traveling towards the cliff is traveling towards destruction as surely as the train that has already gone off the edge and is hurtling towards the earth.
So, living and dying are the same process, divided about a pivot point. It's all the same progression, but flying off the cliff signals a kind of milestone on that journey - an escalation, if you will, of one continuous process. And if you take the view that we are all in the process of dying, you are stretching out that phase of life to earlier and closer to birth. To be fair, then, and to keep the equation balanced, you'd have to also stretch out the very first phase of life to later and closer to death. So, if you want to say that we're all busy dying, then you have to also accept that we're all simultaneously in the process of being born. This is fine with me, since I've made my peace with paradoxes.
One final thought: perhaps the moment of death, itself, is another pivot point, separating one's old life from one's new life.