Dogs that are stressed can show signs of compulsive disorder. This may include chasing their own tail or excessive licking of one or more limbs. As a result of such licking, the area can become raw and itchy, which in turn leads to further licking or chewing.
Cats can be prone to 'wool sucking' which, as the term suggests, involves sucking or chewing on woollen items such as blankets.
Wensley also makes the point that dogs and cats aren't the only species affected:
Parrots, for example, sometimes pull out their own feathers after losing a mate or experiencing some other type of trauma.
Since not pursuing divorce for the sake of the pets isn't usually an option, the PDSA recommends seeking compassionate ways to help pets through these trying times. Minimize disruptions in routine as much as possible.