Prime Reading, Kindle Unlimited, and Kindle Owners' Lending Library, are borrowing programs. You've borrowed those books, and they are removed from your account when you subscription to the program expires.
My experience with KU is that many times books in that program also have their prices drop, sometimes to zero. If and when that happens, I sometimes "buy" the book for free instead of borrowing it, so it stays on my account. There are some authors I've come to enjoy who use KU.
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