To be sure we’re on the same page, a Durable Power of Attorney survives incapacity but does not necessarily become effective only on incapacity. For example, here in Florida they are effective and valid upon execution. You should understand the laws of your state and how they apply to the Durable POA, whether you can have it only become effective on certain conditions. I question the advisability of this approach because it potentially leaves gaps in your estate plan, but that’s something you would need to deal with.
As for what happens to the POA on your death, it will immediately terminate. All powers given to the attorney-in-fact designated in the POA will end. The executor or personal representative of your estate will take over at that point.