My friend and I have agreed to serve, she is primary and myself as
secondary, as executors of a trust of an elderly friend of ours.  We
have not been included as direct receipients of any cash or property
upon her death, nor do we want to be named in the trust.  However,
some people have told us that we will automatically receive a share of
the estate should it not be completely depleted during her lifetime. 
Is this true?  And, if it is true can we designate that her family
receive that amount?

Laws on such matters vary from place to place. Where are you?

We are all Florida residents

First, a trust has a "trustee" not an executor.  The trustee makes
sure the trust asets are distributed according to the terms of the
trust.  A properly set up trust will ensure all the asets are
distributed.  If you are not named in the trust you will not be a
beneficiary of the trust.