Definitely not. The Black Butler series has a set of established themes such as the supernatural elements, the Victorian - era setting, and the complex character relationships. The idea of a 'leashed slave story' is completely foreign to the official canon and is likely a disturbing creation outside of the proper series. It would go against the overall tone and moral framework of the official work.
No. The official Black Butler story focuses on Ciel's journey to avenge his family, his pact with Sebastian, and the exploration of the underworld of Victorian England. There is no place for a 'leashed slave story' in this official narrative. Such a concept is not in harmony with the positive and complex themes that the series is known for, and it is most likely a non - official and inappropriate deviation from the original story.