Does truth of emptiness imply that nothing existent ever ends?
Like the first verse of Nagarjuna's Madhyamikakarika, Prasangika refute the four extremes of production. Nagarjuna says:


  Neither from itself nor from another, nor from both, nor without a
  cause, does anything whatever, anywhere arise.


What is produced is not truly produced (in the sense that it is not inherently produced), and what ceases does not truly cease (in the sense that it does not inherently cease). There is (conventional) production from another, but not inherent (or true) production from another... and there is no production from itself, be it truly/ultimately or conventionality.

You say:


  To my understanding a person is an impermanent ever changing
  phenomenon. That the person is like an illusion that continues from
  moment to moment in this life. If that is so, then how is death
  different?


It's a great question. Death is different in that the mental continuum separates from the body. There is no such separation before death (except in rare cases of powa etc.) That is how death is different from the constant changes that occur in life. Even though no aggregate stays the same from one moment to the next, there is usually no such separation (of the mind stream from the body) before death.

In addition, since the aggregates belong to the same continuum, we can impute the same name on them although they have changed. It is what we do when we look a picture of us at age 10 and say "Look! It's me when I was ten."