Two different problems
An escape means the animal left the pen. A theft means another character took it. Both end the same way: find the animal and put it back in the kennel. Cleaning, feeding, or buying a new pet does not return the missing one.
What to do
- Read the prompt. It tells you the animal escaped or was stolen.
- Leave the desk and search. The missing pet is out in the lot or with the thief, not in the food box.
- Bring it back to the kennel. Clicking the thief once is not always the return step.
- Hire a Guard with Coins when thefts repeat. The guard is the worker described for catching thieves. A Receptionist can greet customers while you are away from the desk.
- Close the yard when a prompt says the dogs need it closed, then go back to care.
What not to spend on first
A second floor does not stop a thief who is already in the current pen. Buy the guard before a cosmetic expansion if animals are disappearing. There is no published theft timer, so react to the prompt you see.
Friends in the 6-player server can help look. The listing says teaming up earns more money. It does not publish a percent bonus.