Off the top of my head, two books that fit these that I’ve loved and enjoyed are:
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The Daughter of Time by Josephine Tey: An inspector, temporarily bedridden, gets drawn into the murder of the princes by Richard III (yes, I know the history is not accurate, but what a fun premise!)
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I Have Some Questions For You by Rebecca Makkai: Protagonist gets pulled into a decades old investigation of a former classmate
Ideally, the protagonist is drawn in out of curiosity, not because they’re hired to do the investigation.
by aronnyc