A big, black cat with listless eyes rested in a cage, not getting up even to greet a visitor to the room.The tag attached to her cage had her name, her age and why she had found her way within the walls of the unwanted — her owner could no longer afford her.About 4,000 animals come under the care of the Forsyth County Animal Shelter each year. Compared to other local rescue groups, fewer cases at the shelter come out with happy endings, as every animal here has been deemed lost, unwanted or unfit for society. There’s little hope in a building that serves as the place where animals are taken from or surrendered by incapable owners.