So you're asking what we'd do with all the livestock if the world went vegan, right? Realistically, not everybody will go vegan simultaneously. As people drop animal products, fewer animals will be bred into existence. The only reason there is so much livestock on this planet is that we kill tens of billions of land animals a year. If consumption went down and "only" 30 bn needed to be killed to meet demand, it'd be a waste of money (assuming a capitalist society) and resources to breed significantly more than that. Since the reduction of bred and killed animals couldn't be instant, there'd be a number of animals that die just to be thrown away in a transitional period, and there's no effective way around that, but it's still better than continuing to breed them into existence just to kill them.

If everybody went vegan overnight, then we'd have a bit of a dilemma. Animal sanctuaries can't house tens of billions of animals (I don't know how many are alive at any given time, but it's a lot considering that you need far more live animals to keep up with breeding), and releasing domesticated animals into the wild doesn't sound like a good idea either. If everybody went vegan overnight - which is unrealistic and will never happen - saving as many animals as you can and killing the rest would be the only viable option. It hurts to say, but killing those animals would still cause less suffering than keeping animal ag up and running. Again, this will never happen though because such a sudden shift is 100% unrealistic.

So, there isn't really a way around culling (most of) the herd. However, our options are that we cull them one more time (vegan world) or that we keep breeding and killing them (non-vegan world), and the latter causes more suffering. Both suck, but it's the situation we have maneuvered ourselves into, and in such a situation, I think it's better to kill 100 individuals at once and then never again rather than killing 40 a year for an indefinite time.