In humans, there is a condition known as Takotsubo cardiomyopathy. This is a rare disorder in which the heart stops working after an emotionally traumatic event such as loss of a loved one, a natural disaster, a terrorist attack, etc…
In wildlife medicine there is a condition known as capture myopathy. This is a condition in which an animal becomes so stressed/frightened that they die after being chased or caught. In fact, there is a real physiological connection between the mind and the heart.
In the conditions mentioned above, there can be a mass release of the fight, flight, freeze, or faint hormones that can have devastating effects on the heart.
The way an animal perceives things can wreak havoc on the animals physical and psychological wellbeing. Treating anxiety disorders helps keeping the heart as healthy as possible for as long as possible; decreasing the anxiety simply benefits the welfare of the pet.
For those of you who are intrigued by the similarities between diseases (both physical and emotional) that humans and non human animals share, we would encourage you to read a book called Zoobiguity written in collaboration with a cardiologist and psychiatrist.