This is because zakah is a purification, and the disbeliever is not eligible for purification except through Islam; nothing purifies him but Islam.
The apparent meaning of the author’s words is that even if a person’s slave is a disbeliever, Zakah al-Fitr is not obligatory with respect to him. This is indeed the case.
This includes males and females, young and old, free persons and slaves.
His statement, “has one sāʿ remaining for the day and night of Eid”: “has remaining” means that he possesses it.
His statement, “its night,” means the night of Eid. “The day of Eid and its night” are both in the adverbial accusative.
His statement, “one sāʿ”: this is the subject of the verb “remains,” and it is the prescribed measure of zakah. The intended meaning of a sāʿ will be explained later. He mentioned a sāʿ specifically because it is the obligatory amount: a person is not required to give more than one sāʿ; yet if he possesses less than a full sāʿ and nothing else, his obligation is not waived. Rather, he gives whatever he is able to give.
Thus, if he has enough to sustain himself on the day and night of Eid, with one sāʿ remaining, he must give it. Likewise, if only half a sāʿ remains, he gives it, for Allah the Exalted says:
“Fear Allah as much as you are able.”
This is like one who finds enough water to wash only some of the limbs required for ablution: he uses it, then performs dry ablution for what remains.
His statement, “beyond his own provision, the provision of his dependants, and his essential needs.”
“His provision and the provision of his dependants” means their food and drink.
“His essential needs” are those things whose presence is needed in