Replace runaway or returned pet
Adopt a pet that is totally identical to the pet you want to bring back. Bring it to your playpen and choose the "Petz" section in your tool bar. Select "Copy Petz" then click on the pet you just adopted. Instead of clicking "Save", choose either "Runaway Pets" or "Returned Petz", depending on whether the pet you want to bring back ran away or was returned. Do not press ENTER. Instead, go back to where you started (while remaining in the "Copy Petz" screen), and select "Adopted Pets". If done correctly, all the names of the pets you currently own should appear on the screen. Choose the "Save" option to get your pet back.