In Florida, like in all states, the power of attorney ends when the principal/grantor dies. A durable power of attorney is a useful document that gives your agent the power to help manage someone's legal and financial affairs during their lifetimes. When the principal/grantor dies, the power of attorney ends. This may mean that the decedent's estate/probate takes over or a number of other possibilities.
The next question: who is in charge upon death? This may mean that the decedent's personal representative/executor would then take over. This may mean that the probate process would then take over. If the decedent had a revocable living trust, the successor trustee takes over and manages the decedent's affairs. You may need legal help with this part of the process, or at least a consultation with a good probate attorney.
You can learn more about probate process with our free handout: Navigating the Florida Probate Process
If you are concerned about the effects of probate upon your death, you may want to establish a revocable living trust for you and your family's benefit.