I think emergency duties should automatically be assigned to everyone who has nothing else to do, and they do something considered an emergency instead of spare time. This might include hunting, or cooking in the case of lack of food, weaponsmithing and armorsmithing when a seige is coming and the soldiers don't have weapons, and brewing (of course).
If this is dine without the player triggering it: baaaaaaad. I can already see the line of untrained hunters rushing out to wrestle the elephants for their delicious meat ^^
If a player can assign emergency status to a job if certan criteria are met thou, I like it. Such criteria could be:
-total food stockpile < number of dwarves = any labour that directly produces food can set to emergency. This would not include cooking because dwarves can eat food raw if they have to, it doenst have to taste good, it has to exist.
-hostiles on map > number of military dwarves*X = military duty can be set to emergency and the soliders will not pause to eat/sleep till they are acutally hungry/fatigued. This does not include wild animals and so on, just real hostiles. Maybe only ambushes, siges and megabeasts count.
Alternatively, instead of setting triggers, you could deter the use emergencies with some sort of downside. A good deterrent could be if any dwarf who was on emergency duty will be on break for at least twice the time afterwards. This way anything could be an emergency, but you cant use the emergency setting to make your dwarves work more all the time.