They already had something like this, it was called exhaustion. If I remember correctly it gave a -50% evade, hit, and fizzle chance if you ran out of stamina, when it was the only sprint resource available.
I would just say they need to fix how stamina is calculated, since constitution gives stamina and classes with a stamina pool are getting their resource from two attributes where as casters are only getting mana from one, which is why stamina and mana are not equal. If you play a melee class in pvp, you may realize that it's quite impossible to ever run out of stamina.
As to focus, I can respect personal opinions, but that's a big NO from me. I already have mana issues, I don't need to go hide out for another resource deficientcy.