But the so-called shelter doesn't have a building. The humane society is made up of volunteers, like Greene, who use their homes to foster pets.
No-kill shelters are spreading across the country. They won't euthanize animals for population control.
"Killing healthy animals just becuase they don't have a home," Greene said.
But she understands that shelters never want to put animals down.
"They do it becuase they believe it's a neccessary evil," she said. "But it's been proven that it's really not neccessary."
The humane society is not funded through Terrell County. They survive on donations alone.
"We're all the time doing some little something."
Eventually, the Humane Society would like to build what they call an animal sanctuary, not a shelter. They're sponsoring a golf tournament and low country boil fundraiser Saturday at the Dawson County Club.
Greene has several dogs of her own, Heidi, Buster and Fritz, along with three cats, all adopted.
"And once I got to that point, I was like, you can't keep them all."
But sometimes, you want to.
"About the time you think there's nobody out there that wants this dog or cat, the right home will come along."