I don't know how things are in Korea but at night there are no humans at the animal shelters where I live. I'm sure there are other shelters where there's always someone there but it isn't unreasonable to say that Bexan was at a shelter where there are no humans at night.
what about cameras
if theres no reason to check them, i doubt that they would check
Nobody checks the camera footage unless there's a reason to do so (if there's a camera anyway, it's just an animal shelter).
im rereading the story and i just noticed but in the beginning of he story, bexan said he was caught and put in a shelter and he decided to stay there for awhile since they gave him food and shelter.... but what happens when he turns human every night?