There is a common misconception that people who witness a Sefer Torah falling to the floor (G‑d forbid) must fast for 40 days.1 How this “fact” became so widespread is a mystery.
The general category of respect for a Sefer Torah is addressed in depth by the classic codifiers of halacha, but there is no mention of the topic of a Sefer Torah being dropped.2 The issue is first discussed at length by the later authorities, who do advocate fasting – either a one day fast; or a series of 3 fasts on Monday, Thursday and the following Monday. The consensus among contemporary poskim is that the person who dropped the Sefer Torah should fast one day (from daybreak until nightfall), and the people who saw it fall to the ground should also fast one day. Members of the shul who were not present at the time, as well as anyone who was in the room but did not personally witness the Sefer Torah fall, should give pidyon nefesh (an amount of money equal to one day’s worth of food) to charity.
note: According to many Achronim it is the prerogative of the local rabbi to determine the most appropriate course of action for his community: Under special circumstances, the rabbi may prescribe pidyon nefesh or a half-day fast (from daybreak until noon), instead of a full day fast.
The purpose of fasting (or redeeming the fast with charity) is to encourage introspection and repentance. The people involved, including the witnesses as well as members of the community, all participated – on some level – in a breach of kavod Sefer Torah. It is important to internalize the seriousness of the matter and actively ensure that Sifrei Torah are always handled with appropriate care and respect.
update: All of the information above is relevant even if the Sefer Torah is pasul. This is mentioned explicitly by many poskim, and is implicit in the words of several others.
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There are other transgressions which require 40 days of fasting (daybreak to nightfall) for penance, but this isn’t one of them. For any of those other transgressions, the 40 days of fasting can be exchanged for one long fast of 2 days straight (from daybreak until nightfall the following day). ↩
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The only situation mentioned by the Rishonim which requires penance for a breach of kavod Sefer Torah is where a Sefer Torah is burned (G‑d forbid) – deliberately, with malicious intent (i.e. not an accidental fire); the witnesses are obligated to tear kri’ah.↩