It would make no sense for a pack animal to hunt on its own. Being in a pack *is* the reason that pack animals ARE dangerous. And to be blunt, most herbivores lack the dentition-or any of the other adaptations-necessary for a creature to eat meat. In order to do that, you typically see long, pointed canine teeth and sharp teeth that are capable of cutting through raw flesh. A deer or horse, for example, simply cannot kill an animal and eat it-they don't have the proper teeth for the job, nor the right adaptations for predatory behavior in the first place.
For a start, binocular vision is an adaptation that predatory animals have since stalking prey involves judging distances-which the wide angle view of horses and other prey animals doesn't allow. It does, however, allow them a much wider field of view than a predator has-which in turn is way for them to spot a predator attempting to sneak up behind them. Then there's the simple issue that animals we would classify as prey animals don't have the hardware required to be reliably able to stalk and kill another animal. The long legs of a deer or a horse are for running AWAY, and don't allow it hide in the grass to stalk prey. And let's not forget, predators typically kill their prey by biting it, often by breaking it's neck and/or by biting so that the animal soon suffocates. A horse, deer, or hell even a camel simply *cannot* do that.
And animals won't eat meat if they're herbivores, since they don't recognize it as being a food source-the only reason that cattle can be fed parts of other cattle is that it's mixed into their feed, which they do recognize as a food source.
Bottom line: what you are suggesting is a physical impossibility. Herbivores eat plants not because they have vegan morals, but because it's their food source and what they've evolved to extract nutrition from. Obligate carnivores are the same with meat-an obligate carnivore won't eat any plant matter, period, because they CAN'T DIGEST IT. You can have hungry carnivorous animals, but that is about it (A hungry herbivore would eat the grass or shrubs, or starve). Eventually, animals will need to eat anyway as I understand it.
By the way, keep in mind if a omnivore or carnivore is starved enough to attack anything it sees on sight, it would be a weakened and desperate animal-animals do use risk assessment when evaluating whether or not to go after a particular prey, and typically will pick the easiest thing to kill and eat. And if they can smell a kill, they might just go and wait until the animal which made the kill is finished, then scavenge what is left.