[The poor person upon whom Zakāt al-Fiṭr is not obligatory]

Answer—and Allah is the Granter of success: The poor person who possesses only the expense of the Day of ʿĪd has no Zakāt al-Fiṭr due upon him. The proof is the Prophet’s—May Allah bless him and his family and grant them peace—saying, “Spare them from begging on this day,” which indicates that whoever has only the expense of the ʿĪd day for himself and those he supports does not have the charity due.
The jurists of the madhhab said: The poor person who does not possess, beyond the provisions of ten days for himself and those he supports, anything more—does not have Zakāt al-Fiṭr obligatory upon him. Whoever possesses more than that has it obligatory upon him; and he is not obligated to pay the charity except from what exceeds the expense of ten days.
Source : Min Thimār al-ʿIlm wa al-Ḥikmah vol.1