What is to be done if someone swore to do something but then became unable to do it and fell asleep, and this has happened to them many times; does an expiation for an oath (kaffarat yamin) become obligatory upon them?

According to the majority of scholars, you must offer expiation for each oath. If you do not know their exact number, then act based on your best judgment and expiate what brings you certainty or a strong presumption of being absolved. The Hanbali school of thought holds that a single expiation suffices for all such oaths. The expiation consists of feeding ten poor persons, clothing them, or freeing a slave. If you are unable to do any of these, then fasting for three consecutive days is more cautious.