Generally this happens in young animals, and occurs more commonly with canines. It is seen more frequently around the holiday time with decoration lights; but can occur at any time that a pet has access to an electrical cord.
It can result in a wide range of problems. Locally there can be direct trauma to the tissues of the mouth, especially the tongue and lips. The duration of chewing time will affect the severity of damage.
Not all complications will be visually evident or occur right away. The electric shock can alter the heart rate/rhythm. This can affect blood pressure, and also trigger fluid to build up in the lung tissue causing breathing difficulties. Brain activity can be altered resulting in seizures or other abnormalities.
No matter what symptoms are evident, any pet that is found chewing on or is thought to have chewed on an electrical cord should be examined right away by a veterinarian. In addition to the exam and checking vitals, an x-ray or other diagnostics may be recommended. Your pet may need Oxygen or other supportive care.
It is best to prevent this from happening by covering exposed cords. Hardware stores now carry plastic channels that create a tunnel around the cord. Keeping puppies crated or in an exercise pen when they can’t be directly supervised is another option. Confining kittens to a different room is another option.