o    If an executor dies, the will is still valid.  If he/she dies before you, or after you but before obtaining probate of your estate, the other executors (if you have named more than one) take on the task.  If this leaves you with no executor, one or more of the beneficiaries will have to apply for 'Letters of Administration with the Will Annexed'.  The other beneficiaries will have to consent.  Sometimes there may be a dispute about who should do the job and the Public Trustee would then be appointed as Executor.
o    If one of your executors dies after you and after obtaining probate of your estate, the other executors continue the task.  If there are no other executors, the executor of the deceased executor takes over both your estate and the deceased executor's estate.