Normally, if the executor dies testate, the representation passes to the executor of the first executor's estate upon probate of the latter's own will.
Slayer statutes provide a right of civil action to a victims successors for the purpose of directing the victims testate/intestate property away from the slayer.
If, however, you join them as tenants-in-common, then on your demise your interest passes to your estate, which would have to be administered either as a testate or intestate estate.