Vegetarian, Vegan and Animal Rights

https://motherboard.vice.com/en_us/article/jpgddd/the-red-wolf-is-mostly-coyote-conservation-endangered

By conducting whole-genome sequence analysis on 28 canids—including gray wolves, red wolves, eastern wolves, coyotes, and even domestic dogs—the team found that the red wolf is about 25 percent gray wolf and 75 percent coyote, while the eastern wolf is about 50 to 75 percent gray wolf, and roughly one quarter coyote.

So although it is possible for them to go "extinct" it would also be possible to bring them back with some Wolf/Coyote breeding, you would just need to get the above ratio correct.