Nexallus
From Takeda to Robin
In exhaustion state, you CAN'T:Chip, or more chip, seems to be the general consensus. Still, unless the out of Stam state becomes more damning (some just dash away), health dmg seems to be a better option imo.
Roll away, Safely Parry, or Safely Attack
The only safe option you have in exhaustion is blocking (dogding can be guard broken), and adding stamina damage on block makes blocking more of a neutral tool, rather than a get-out-of-jail free card.