Hello, thank you for this interesting question. There are already ways to feed carnivorous pets vegan diets, however these can be difficult to maintain as dogs in particular have very specific dietary needs depending on their size, breed, etc. For these reasons, people feeding their carnivorous pets plant based food must formulate their diets extremely carefully to ensure they’re getting all the nutrients, proteins, fats, etc. that they need to be happy and healthy.
Luckily, more and more brands are beginning to produce vegan products for traditionally carnivorous pets which makes keeping the balance a little easier. As an example, here is a link to a vegan cat/dog food retailer: https://www.ethicalpets.co.uk/vegan. Their ingredients should help you understand what we would feed our pets if the whole world turned vegan tomorrow.
Interestingly enough, one of the UK’s longest living dogs, a collie by the name of Bramble, lived to 25 years old on a vegan diet!! Here’s a link with more info on that: https://thrivecuisine.com/lifestyle/vegan-dogs/bramble-vegan-dog/
It’s worth noting that any change to a pets diet should be done gradually to avoid issues and a major change such as transitioning from a carnivore to a vegan should be discussed with a trusted vet, but that obviously wouldn’t be possible in this hypothetical situation.
I hope this answers your question
Please reject the advice from the commenters suggesting to feed your cat a vegan diet. Cats are obligate carnivores and must have meat in their diet to survive-there have been instances where a cat or kitten was fed aa vegan diet and became so ill they almost died. Here is a short article about why cats can’t survive on a vegan diet: https://www.aspca.org/news/why-cant-my-cat-be-vegan
Do you mean just the human population would go vegan? Or do you mean eliminating all carnivores? That wouldn’t be possible, as carnivores keep the eco systemin balance by removing sick and weak animals.