This article states that animals that are no longer wanted by their owners are dropped off at animal shelters where they are sheltered and cared for but only temporary. Only about half of the animals that show up at a shelter will find a new home. The rest euthanized. There are approximately 5,000 animal shelters in the U.S. They are nonprofit agencies usually run by local governments. They will take about every type of domestic animal, about 7 million dogs and cats are taken in by shelters each year. Some animals are brought in by there owners and others are brought in by animal control officers that are found roaming the streets. How long an animal can stay is based on the individual shelter rules.
Not all homeless dogs and cats go to a shelter some go to animal rescue groups that specialize in a specific breed. The animals normally come from questionable breeding centers that have been shut down. Unlike shelters they don't normally have facilities to house the animals so they have volunteers that care for the animals until they are adopted. There are also animal sanctuaries, which are large areas of land that care for dogs, cats, goats, donkeys, cows, pigs and other larger animals. Some animal sanctuaries even keep wild animals, like lions and tigers. These animals will most likely spend there whole life in the animal sanctuary without ever being adopted.