Nearly everyone who has worked at the intake area of an animal shelter understands that most of the problems for which pets are surrendered are not pet problems, they are people problems. Accepting these pets to shelters without addressing those problems results in a destructive and vicious cycle that is depicted in the graphic below.
It starts when a family unwittingly creates a medical or behavioral problem with their pet. As a result, they surrender the pet to an animal shelter, where little is generally done to uncover or solve the real reason for surrender. The people then go out and get another pet and the problems starts all over again, because the people have learned nothing through their interaction with the shelter.
The goal of a good pet retention program is to break that cycle through a heartfelt intervention that uncovers the real reasons for pet surrenders and then helps people to resolve the problems without getting rid of their pets. This reduces the number of animals entering animal shelters while helping people become better care givers to their animal companions.
A good overview of how pet retention programs work is provided in the short video at No Kill Learning.