The clones have 10hp. It's just not shown.

There is technically a third HP stat that is not visible in any of the UI in Dust. That's the base HP of your clone body. It's about 10 HP if I recall correctly. Even if your armor is down to 0, there is a chance your clone may have survived and you can continue fighting until your naked clone somehow suffers a hit from a stray bullet which then puts you into a bleedout phase. It has happened and still does with regularity. You may have noticed it happening to yourself at one point. It has for me.

I'm guessing that since 10 HP is extremely small, CCP probably didn't think it was necessary to have it as a visible stat at the time and that you would likely be dead anyways if your clone body got scraped by a bullet after your armor reaches zero.

Eve Online on the other hand uses the hull HP instead. Your ship is basically a hull with armor plates and shield installed on top of the hull. It is generally believed that if the hull is breached, your ship is gone and you get ejected. Your pod has the same thing except that if the hull is breached, your clone body is automatically dead because all that is standing between your clone body and the vacuum of space is the hull of the pod.