The element doesn't disappear.
The half life is regarding the radioactivity of the element. So for example if substance A had a half life of 5 minutes, and at time 0 was emitting 20 units of radiation per second, after 5 minutes, it would be emitting 10 units, after 10 minutes, 5 units etc.
What usually happens is that the element decays into another, ore stable, form of that element (eg from uranium 238 to Uranium 232) <- numbers may be wrong, can't remember.