Yahya related to me from Malik from Nafi that Abdullah ibn Umar used to pay the zakat al-fitr for those slaves of his that were at Wadi'l-Qura and Khaybar.
Yahya related to me that Malik said, "The best that I have heard about the zakat al-fitr is that a man has to pay for every person that he is responsible for supporting and whom he must support. He has to pay forall his mukatabs, his mudabbars, and his ordinary slaves, whether they are present or absent, as long as they are muslim, and whether or not they are fortrade. However, he does not have to pay zakat on any of them that are not muslim."
Malik said, concerning a runaway slave, "I think that his master should pay the zakat fo rhim whether or not he knows where he is, if it has not been long since the slave ran away and his master hopes that he is still alive and will return. If it has been a long time since he ran away and his master has despaired of him returning then I do not think that he should pay zakat for him.'
Malik said, "The zakat al-fitr has to be paid by people living in the desert (i.e. nomadic people) just as it has to be paid by people living in villages (i.e. settled people), because the Messenger of Allah ﷺ made the zakat al-fitr at the end of Ramadan obligatory on every muslim, whether freeman or slave, male or female."

حَدَّثَنِي يَحْيَى، عَنْ مَالِكٍ، عَنْ نَافِعٍ، أَنَّ عَبْدَ اللَّهِ بْنَ عُمَرَ، كَانَ يُخْرِجُ زَكَاةَ الْفِطْرِ عَنْ غِلْمَانِهِ الَّذِينَ، بِوَادِي الْقُرَى وَبِخَيْبَرَ . وَحَدَّثَنِي عَنْ مَالِكٍ، أَنَّ أَحْسَنَ، مَا سَمِعْتُ فِيمَا، يَجِبُ عَلَى الرَّجُلِ مِنْ زَكَاةِ الْفِطْرِ أَنَّ الرَّجُلَ يُؤَدِّي ذَلِكَ عَنْ كُلِّ مَنْ يَضْمَنُ نَفَقَتَهُ وَلاَ بُدَّ لَهُ مِنْ أَنْ يُنْفِقَ عَلَيْهِ وَالرَّجُلُ يُؤَدِّي عَنْ مُكَاتَبِهِ وَمُدَبَّرِهِ وَرَقِيقِهِ كُلِّهِمْ غَائِبِهِمْ وَشَاهِدِهِمْ مَنْ كَانَ مِنْهُمْ مُسْلِمًا وَمَنْ كَانَ مِنْهُمْ لِتِجَارَةٍ أَوْ لِغَيْرِ تِجَارَةٍ وَمَنْ لَمْ يَكُنْ مِنْهُمْ مُسْلِمًا فَلاَ زَكَاةَ عَلَيْهِ فِيهِ . قَالَ مَالِكٌ فِي الْعَبْدِ الآبِقِ إِنَّ سَيِّدَهُ إِنْ عَلِمَ مَكَانَهُ أَوْ لَمْ يَعْلَمْ وَكَانَتْ غَيْبَتُهُ قَرِيبَةً فَهُوَ يَرْجُو حَيَاتَهُ وَرَجْعَتَهُ فَإِنِّي أَرَى أَنْ يُزَكِّيَ عَنْهُ وَإِنْ كَانَ إِبَاقُهُ قَدْ طَالَ وَيَئِسَ مِنْهُ فَلاَ أَرَى أَنْ يُزَكِّيَ عَنْهُ . قَالَ مَالِكٌ تَجِبُ زَكَاةُ الْفِطْرِ عَلَى أَهْلِ الْبَادِيَةِ كَمَا تَجِبُ عَلَى أَهْلِ الْقُرَى وَذَلِكَ أَنَّ رَسُولَ اللَّهِ ﷺ فَرَضَ زَكَاةَ الْفِطْرِ مِنْ رَمَضَانَ عَلَى النَّاسِ عَلَى كُلِّ حُرٍّ أَوْ عَبْدٍ ذَكَرٍ أَوْ أُنْثَى مِنَ الْمُسْلِمِينَ .