One common theme is redemption. Since Ash has a complex past, many fanfictions focus on him finding redemption through his relationship with the reader. Another theme is the exploration of power dynamics. Ash has a certain power in the Black Butler world, and how that interacts with the reader is often explored.
One popular 'Black Butler Ash x Reader' fanfiction is 'Ash's Redemption'. It shows an interesting take on Ash's character and his relationship with the reader. Another is 'In the Shadows with Ash' which has a great plot that involves mystery and some sweet moments between the two.
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.