Can a sixteen year old legally move out in georgia without parental consent?

my cousin is sixteen years old. her mother has large mental issues and constantly threatens her, and always telling her what a f**kup she is, everything is her fault,etc. they have gotten into fistfights before and my cousin is literally scared for her safety. it is plain to see that it is not a healthy environment for my cousin, and it is steadily draining her mental stability. she has turned to bad friends and drugs to help cope with the stress of her own home in the past. i have heard that sixteen year olds can move out as long as they have a place to stay, and she does. her mother let her move in with us, and broke into our house randomly one morning and stole her away saying if she didnt come shed call the law on her and declare her an unruly runaway and send her to YDC. is it true that she can legally leave her mother?