When a bonded pet dies, it turns into a "pet ghost".

This ghost can still obey the movement commands (follow, come, etc.) of its living master but can not be commanded if the owner is also dead. The pet ghost will not dissipate or lose loyalty, but cannot be stabled.

Any player can attempt to resurrect the pet with bandages if they have at least 80 skill points in Veterinary and Animal Lore. The pet owner or a friend of the pet must be nearby to confirm they want the pet to be resurrected. Pets suffer skill loss of 0.1 skill points per skill each time they are resurrected. The penalty of increased skill loss if someone other than the owner resurrects the pet has been removed with publish 19.

The chance to succeed when resurrecting a pet (providing you have 80+ vet/lore) is calculated as follows:
(100 * (veterinary * 10 - 930) / 50 + 500) / 10

Pets that have not bonded to their owner will not turn into a ghost and are lost forever once they die. If you release a pet ghost, it will disappear with no chance of recovery.