Would starvation cause a wild animal that was an herbivore to kill and eat meat?

Herbivores are quite specialized to eat plants. That's fantastic, because eating nothing but plants takes a lot of specialization. Plants are tough to digest, and lack a lot of amino acids, so an animal has to be built to deal with eating a lot, digesting for a long time, and not worrying about dietary deficiencies.

That also means that being good at one thing necessarily means that they're bad at other things. A starving cow isn't going to go looking for meat, it's just going to keep looking for grass until it dies. It can't run fast enough to catch anything.

It doesn't have a good way to kill prey. It doesn't have sharp incisors and cuspids to cut into the meat even if it had some available. Further, it just doesn't think meat is food.

Even if it were somehow able to hunt - say very slow, very squishy, blind animals lived near it - the cow would still be better off looking for plants to eat. It's so good at eating plants, and so bad at eating meat, that even a relatively easy to catch animal would be much less efficient for the cow than simply looking around more for some plants. If it did find plants, it would be back to 100% efficiency.

All the time it might spend trying (probably unsuccessfully) to catch and eat an animal would just be time NOT spent eating plants. To make it a little easier to understand, think of an unarmed person in the wild. If you know that there are edible fruits and nuts in the area, but there are also badgers, no matter how hungry you are, you're better off looking for fruits and nuts than wasting your time trying to hunt a badger.

It's possible that you could catch and kill a badger, but it would be time consuming, dangerous, and far from certain. Then if you did catch one, it would be very difficult to eat raw. On the other hand, you can keep looking for your fruits and nuts.

As soon as you see one, you're guaranteed to be able to catch it without it running away or fighting you. You know that it's safe to eat. And you don't have to work very hard to find them, you just have to be patient.

Herbivores are experts at slow and patient, low effort, low risk eating.