Do libraries conduct inventories? If so, how often, usually?
I ask this because I found a wonderful new historical mystery series and am stuck at the first book. When I first made the list of all of the titles in the series, I went online to the local library's website and searched for all of them to see what my chances were of being able to read most, if not all, of them through the library. Out of approximately 20 books, only 2-3 were not at the library. I thought, great! I'll see if I can get those 2-3 on my Kindle and be able to read the whole series. So I requested book 1 from the library and when I went to pick it up, I saw how small the book is and decided to go ahead and get book 2. I looked up where to find it in the card catalog (which showed that the main branch, where I go, was the only branch that had a copy) and the system said it was on the shelf under mysteries. I checked there. Found a bunch of the other books by the author, but not book 2. I went ahead and checked the general fiction area because I know books are occasionally misshelved. No big deal, but it wasn't there either. I explained all of this to the librarian as I checked out book 1 and he said he'd place a hold on it and that might prompt the book to be found.
On Monday I decided to look at my library account to see if the book was available yet and they just hadn't called me. The book was still showing as requested, but instead of the book cover image that should've been there, it was a plain blue square. Something then prompted me to look up the book in the online card catalog. Not there.

Now I have no way to read book 2 unless I spend money for a physical copy of the book since it's not at the library (not even in the Orleans Parish system either) and that particular book is not available on Kindle. I don't want to spend money on a book I don't intend to keep.
After all that, my question is, again, do libraries conduct inventories at all so that they know when a book is completely gone from the library and can then be removed from the system?