Public Service Announcement: Contrary to popular belief, it is actually not really physically possible for you, your dog, or any other mammal to actually vomit up their stomach. It may seem like they are trying, and they probably feel like they have succeeded. But I promise you with 99.99999% certainty that the fluorescent pink object that was brought up by your dog at 2 AM is not, in fact, his stomach. It is likely your teenage daughter's completely inappropriate underwear, with perhaps a bit of Alpo thrown in for good measure. So when you show up at the ER at 3 AM, hysterical over the missing organ, please forgive me when I don't seem as worried as you expect. You've told me that your dog now must have "an empty tube" draining kibble into the abdomen, which will of course cause him to bloat [in a stomach that you suspect is no longer there?!? Oy.] I'm sure you did read it on the internet. I really do appreciate* your effort to solve the puzzle for me prior to presentation by contacting Dr. Google, since I am such a fresh-faced young doctor. However, I promise that (barring any severe trauma, of course), there is still a stomach at the end of that esophagus, so he won't be needing that theoretical gastric prosthesis that you found while Googling on your smart phone. I'll just wheel him into the OR, cut the matching bra and socks out of his jejunum, and he'll be well on his way to recovery. Or perhaps some more underwear-eating.
*Sarcasm. Just another service we provide!