Folders with permissions 777 can only be deleted by someone else if the parent folder allows it.
Example:
/home/user = 755
/home/user/tmp = 777
/home/user/tmp/temp = 777
A different user can only delete /home/user/tmp/temp, not /home/user/tmp.
Note: removing a directory is performing a write action in its parent directory.
Note also: any file in /home/user/tmp/temp can be removed, even if it has permissions 600; rm will ask to confirm the override, but it will be granted.