I know multiple people who reported their expiring passport as stolen, just to be able to keep it (usually for purposes of having proof that they've held certain visas in the past).
Eh, you want to watch out doing that - some countries get real suspect if you have ever reported a passport stolen in the past.
It's definitely a thing across various ex-Soviet countries, and likely others as well.
My girlfriend needed her old passport for travelling with an Interrail train ticket because the passport expired between the time of ordering the tickets (and submitting the document number) and travelling.