I worked at a vet clinic years ago and we had a cat escape. We looked for months, and assumed it had somehow gotten outside and got away. Then one day someone made one last trip to the groomer's room after the lights had been shut off for a few hours and swore she saw a black cat dart under the bathtub. I can't remember if we lured him out with some food or set a live trap, but we ended up catching him and returning him to his owner after fattening him back up.

So, there is still hope for Jack yet...