The shelter from which I adopted Cassie is a former three-flat with a small back yard, so sometimes people don't even call but literally drop cats off at the back door. They are almost always at (or over) capacity. When a cat is dropped off, though, there's really nothing they can do except start the admitting process. They ask for a donation when a cat is placed with the shelter to help with the admitting expenses - I think sometimes people drop cats off when they can't afford to make a donation.