A half life is a probability defining when 50% of an element is expected to decay. Its possible that all of the element decayed or that none of the element decayed, but this is extremely unlikely. Think about it this way, if you flip a coin two times you can get 100% heads, 50% heads, or 0% heads. But as you continue to flip coins, say you did it 10,000 times, you will get about 5,000 heads and 5,000 tails because probability tends to balance large numbers out to represtent their expected proportion.
The second half life is when 50% of what is left over decayed. Mathematically speaking, it would take a very long time for all of an elemental material to decay. You'd go from billions of atoms of material to two atoms, then one half life later one decays leaving you with one atom. And that last atom would have a 50% chance of decaying by the next half life.
Quantum physics introduced probability into physics, and probabilities are what we are dealing with here.










