During the scenes in the pound, we see a dog being led off to another room, where it's heavily implied the dog was put to sleep. They never outright say it, but Lady turns to the other dogs and says "You...you mean he's...?"
Trusty's Disney Death. Jock whimpering, then when he nudges Trusty and there's no response, he looks up at the sky and lets out a mournful howl.
It would've been even worse had the filmmakers gone with the original plan to kill him off for real. Fortunately, they decided against it.