Is Zakat al-Fitr due for slaves owned by a slave?

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If it is held that a slave cannot possess property through ownership (tamleek), then Zakat al-Fitr for the sub-slave is incumbent upon the main master, as the sub-slave remains his property. This is the apparent view in the statement of Al-Khiraqi, Abu al-Zinad, Malik, Al-Shafi'i, and the People of Opinion. The sound position is that their Zakat al-Fitr is obligatory because it follows maintenance, and maintenance for the sub-slave is obligatory upon the main master; therefore, their Zakat al-Fitr is also obligatory, and complete ownership is not a condition for its obligation, as demonstrated by the obligation of Zakat al-Fitr upon a mukatab (partially freed slave) for himself and his slaves, despite his incomplete ownership.