Torn Covers of Seforim: Are they Tashmishey Kedusha

When the cover or spine cover falls off a sefer and is no longer useable( i.e. to reaffix it to the sefer) does it has to be put in Geniza?

The Rav told me that it goes in Geniza.

We once had an old sefer and the spine was shedding a little. That didn’t need Geniza.