I would expect to see pockets of domesticated animals survive in captivity across the world for various non-meat purposes. Even if all captive breeding is banned, I would still expect allowances for governments or organizations to maintain breeding populations as a living reminder of where our civilization came from.
Right. I've seen some zoos that already have a little "farm" section showing off some local heritage livestock breeds. I'd expect that sort of thing to take right off if it started to look like there was real risk of extinctions.