Can a school or library hand out copies of sheet music to students and keep their copies of the originals (as long as they had enough copies for each performer) to prevent the loss of the originals? The copies would be destroyed after the performance.
One of my all-time favorite TV shows is Gilmore Girls.
Aside from being the origin of many expressive phrases ("Oi with the poodles already!"), as a parent, Gilmore Girls gave me a concept I used almost daily: "jam hands."
What is the origin of "jam hands"? In Season 2, Episode 5, “Nick & Nora/Sid & Nancy”, the perpetually grumpy "Luke" character, upon being confronted with the prospect of childcare, confesses to a distaste for children: because they are loud, because they are messy, and because their hands always seem to be coated in jam.
I have two kids. "Jam hands" are very real.
My oldest kid (15, as of this writing) has paid his dues playing violin and piano, so I have personally witnessed the damage "jam hands" can do to instruments and music. It must be jam warfare out there.
And of course, a kid can lose sheet music simply by putting it in their backpack.
I don't know if “jam hands” and possible “backpack black hole” are the big reasons for this member wanting to give students back-up copies while retaining the "real" ones in a file, but I suspect that is at least part of the rationale. Why wait until the good copies get destroyed or go missing? Why not make back-up copies in advance? If "fair use" creates educational exemptions to infringement, isn't this a use that qualifies?
Sadly, when Congress developed the "fair use guidelines" for educators, they did not invite any parents to the advisory committee, and so the "jam hands" and "backpack black hole" clauses did not make it into the final guidelines. Instead, those guidelines specifically prohibit copying for performance, except for:
Emergency copying to replace purchased copies which for any reason are not available for an imminent performance provided purchased replacement copies shall be substituted in due course.
So: no copying in advance…but, in the face of an "imminent performance," copying to replace "unavailable" purchased copies is okay (provided the replacement copies are "substituted in due course").
What does this tell us? In this case, it's better to be re-active, than pro-active. When a student jams up or black holes a copy, an educator can make replacement for a performance. Just make sure you get around to purchasing and substituting (instead of destroying) those "replacement copies," in "due course."
I would of course love to leave this answer right there, having dispatched sage wisdom and quoted from decades-old guidance from Congress. But I have no doubt that by now, at least one reader has said "Well, what's 'due course'?" And I don't want to be accused of fraternizing with the tomato.
As I am sure any music teacher reading this knows (but what was news to me), these days teachers can often print sheet music on demand (for a price). And while of course not every copy a school has in print is available for download, the "emergency" aspect of the clause quoted above loses some heft when a copy can be obtained for $2.25 online.
THAT SAID, I know music program budgets rise and fall on nickels and dimes. I am not suggesting that a teacher or librarian solve this problem by simply immediately buying new copies; rather that when it comes to deciding what amount of time is "due course," the answer is: no later than when you can make the replacement purchase as part of your next budget cycle.
That said, before stressing about fair use and "replacement copies" and "due course," always check the fine print on the music (and on copies available from other sources). While on my sheet music web site tour, I noted that some (but not all) of the sheet music I saw for sale had the phrase "this copy may be reproduced by the purchaser," and other flexible licenses. So, for each piece of music you want to copy, before you worry, check the fine print. You might have more permission than you think.
I wish I could give a better answer in the fight against “jam hands.” But at least your answer didn’t fall into a “backpack black hole!”
 The full quote is here: https://www.tvfanatic.com/quotes/me-raising-a-kid-i-dont-even-like-kids-theyre-always-sticky/
 Don't watch your kid do this. It's addictive.
 Another beloved Gilmore Girls reference
 For instance, Gerald Ford is no longer President.