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 is His slave and Messenger.
In fact, expiation is due when one breaks his binding oath. However, if a person swears that someone else must eat something and this person does not eat; if his intention was binding him to eat and he does not, the oath-taker is obliged to pay expiation for breaking that oath. However, if his intention was merely to show hospitality and generosity to this person, scholars held different opinions regarding whether or not he is obliged to pay expiation. The preponderant opinion is that he is not obliged to pay expiation since the hospitality and generosity have been shown and the oath has not been broken in this sense. Shaykhul-Islam Ibn Taymiyyah said, “The oath is not broken if a person swears an oath that someone should do something, but the latter does not fulfill the oath. This is so if the intention of the oath-taker was merely to show hospitality and generosity and not binding him to do that act.” What Shaykhul-Islam Ibn Taymiyyah said in this regard is called specifying the oath with the intention (or the reason that caused the oath to be taken). This view is adopted by many scholars, referring to it as the “Bisaat” (context of the oath), or the reason for taking an oath. If the oath-taker does not break his oath, no expiation is due on him, as it is known.
Allaah Knows best.