It is not clear to me why old prayer books and other such works cannot be thrown away once they’re no longer fit for use. I can understand why as long as they’re being used they should be treated with respect given their purpose, but once that’s no longer the case what’s the problem with throwing them away?
What makes prayer books and other such books of Torah learning sacred is not just their purpose, namely for prayer or for learning, but also, and perhaps more importantly, it is their content.
Prayer books have not only many, many verses from the Tanach that are interwoven throughout the prayers, as well as entire sections which are passages from the Torah itself like the “Shema”. They also have many of the various names of G-d Himself. This makes the prayer book sacred even after it’s no longer used.
The same thing applies for books on Torah subjects. Usually they have verses, often they have G-d’s names. And even if they don’t have either, the ideas expressed therein are ideas of holiness and it is not appropriate to throw away such ideas even after the book is no longer usable.
Also, in both cases, while the text may not be usable in its entirety, it still has sections with verses, G-d’s names or Torah ideas that are intact, and those sections maintain their sanctity such that they may not be thrown away.
So what is done with such out-of-use texts? Known by some as “Sheimas”, which is an Ashkenazi pronunciation of the Hebrew word “Shemot” meaning “Names”, they are put in what’s called in Hebrew “geniza” which means “in hiding”. This may be in a closet, a special storage room, or even buried underground.
In times of old, they were often stored in special vaults in the synagogue, thanks to which many old and sacred works have been recovered, which has been of great religious and academic importance. A notable example of this is the famous Cairo Geniza. In modern times, most “sheimas” or “geniza” are buried, either in special sites, or even interred in graves with families’ permission. This later option spares valuable resources for the living while creating a mitzvah which envelopes the deceased in a type of spiritual shroud.
I heard a story once of a person visiting a foreign country who had a bill of the local currency fly out of her hand because of the wind. In chasing after the note she stepped on the bill to keep it from getting away. This was observed by a policeman who summarily issued her a fine for placing her shoe on the visage of the country’s king that is on the currency.
If nations take so seriously the picture of mundane kings on money, all the more so we must take seriously the Names and Knowledge of the King of Kings in our holy books.