The "fossa arenaia" is the large cross shape depression in the center of the arena. In Roman times, this area would have been covered with wooden planking and stored the caged animals and equipment for staged presentations. Under a renovation, this area received a water proofing lining and then apparently flooded with water for some events.
While death was the central theme of the Amphitheater, make no mistake about it, it was also about theater (and making money). Wild animals from Asia and Africa were imported to make spectacular entertainment. Gladiators that fought animals were given the special name of "Venator"
By the late 400's AD the amphitheater was no longer in use and its wall became the source for the raw material to construct other buildings.