Any successes beyond the last damage box are lost.
Unless you are using the Ludus Magnus benefits (https://arenarex.wikia.com/wiki/Ludus_Magnus
Flourish : Passive Ability - Ludus Magnus gladiator models in your cohort earn 1 Favor if, during an attack or counterattack they reach the bottom of their damage tree and still have one or more unapplied net successes.
So a Ludus Magnus gladiator model will receive 1 favor if they have any remaining net successes beyond their damage tree.
Hope this helps