Unless the pigs have been deprived of food and are desperate, it's unlikely they will eat the tomato vines or anything else harmful. Pigs are pretty much people, in terms of what they can eat. That doesn't mean they will drop dead if they nibble on some tomato leaves, any more than you would drop dead from it. I mean, they're poisonous to goats, too, but goats can handle them if they're not the only food offered. They will eat all the ripe tomatoes they can find but probably won't eat the stuff you'd like to get rid of.

My pet pigs eat MIZOORI pig chow as a staple diet and get veggies with that as well as fruit. But they love the leaves that I prune off my tomato plants. So far no ill effects and one of my pigs is 16 years old.