All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
If one swears not to do an unlawful thing, he should fulfill his oath and abide by it out of obedience to Allaah The Almighty and in avoidance of what is unlawful. If he is overpowered by his desires and does what he has sworn not to do, an oath expiation becomes due on him. In his Al-Mughni, Ibn Qudaamah said: “There is no disagreement over this issue among the scholars of Fiqh in different regions.” He also reported from Ibn ‘Abd-Al-Barr that there is scholarly consensus on the obligation of expiation. The expiation for breaking an oath is to feed or clothe ten needy persons or free a slave. If one could not find (or afford that), he should fast three days in response to the Command of Allaah The Almighty (which means): {So its expiation is the feeding of ten needy people from the average of that which you feed your [own] families or clothing them or the freeing of a slave. But whoever cannot find [or afford it] – then a fast of three days [is required]. That is the expiation for oaths when you have sworn. But guard your oaths.} [Quran 5:89]
If you are sure that you are incapable of feeding or clothing needy people or freeing a slave, then you could take resort to fasting as stated by Ibn Qudaamah in Al-Mughni: "If one finds (or could afford for) nothing of those three, it will suffice him for fulfilling the obligation to fast three days consecutively. That is, if he is incapable of feeding or clothing needy people or freeing a slave, he could then resort to fasting three days because Allaah The Almighty Says (what means): {Allaah Will not Impose blame upon you for what is meaningless in your oaths, but He Will Impose blame upon you for [breaking] what you intended of oaths. So its expiation is the feeding of ten needy people from the average of that which you feed your [own] families or clothing them or the freeing of a slave. But whoever cannot find [or afford it] – then a fast of three days [is required]. That is the expiation for oaths when you have sworn.} [Quran 5:89] This matter is indisputable.
As for the criterion of financial incapability, it is, according to some scholars, to have nothing beyond the daily sustenance of the person and those whose financial maintenance is due on him. According to others, it is the person’s being an eligible Zakah recipient.
Ibn Qudaamah said in his Al-Mughni, “One could make expiation by fasting if he does not have, beyond the sustenance which suffices him and his dependents for a day and a night, what is sufficient for expiation. … The criterion that is to be considered here is that the person does not have, beyond the sustenance that suffices him and his dependents for a day and a night, what is sufficient to make expiation with. That is the opinion of Is-haaq, and a similar opinion is adopted by Abu ‘Ubayd and Ibn Al-Munthir . According to Ash-Shaafi‘i if someone is of those who are eligible to receive Zakah under the Sharee‘ah on account of his dire want and destitution, then fasting will suffice him concerning fulfilling the obligation because he is poor.
Hence, if you are of those to whom giving Zakah is lawful, it will be permissible for you to leave feeding and shift to fasting on the basis of the opinion of Ash-Shaafi‘i, which is not the one held by the majority of scholars.
Allaah Knows best.