There are situations other than the prescribed month of Ramadhan, where fasting ‘Siyam’ is advised as a mode of atonement. This could be atonement for breaking an oath or murder of a believer, as ordained in following Ayahs:
‘’God does not hold you accountable for your unintended oaths, but He holds you accountable for your binding oaths. The atonement is feeding ten needy people from the average of what you feed your families, or by clothing them, or freeing a slave. Anyone who lacks the means shall fast for three days. That is the atonement for breaking your oaths when you have sworn them. So keep your oaths. Thus God makes His Revelations clear to you, that you may be grateful’’ (5:89)
The accountability is for oaths with serious intent and not for frivolous oaths. In case an oath with serious intent is broken, a parson with means may feed ten people—the measure of feed is strict, the measure you feed your families with, or they could be clothed, or a slave freed. For persons without means, the atonement is fasting for three days.
For the murder of a believer by error, the atonement is much more severe, as noted in the following Ayah:
‘’Never shall a believer kill another believer, unless by error. Anyone who kills a believer by error must set free a believing slave, and pay compensation to the victim’s family unless they remit it as charity. If the victim belonged to a family who are hostile to you, but is a believer, then the compensation is to free a believing slave. If he belonged to a people with whom you have a treaty, then the compensation should be handed over to his family, and a believing slave set free. Anyone who lacks the means must fast for two consecutive months, by way of repentance to God. God is All Knowing, Most Wise’’ (4:92)
The Holy Ayahs noted above make clear that fasting is a mode of atonement for persons without means, should they ever break a serious oath or commit the murder of a believer by error.