I've reported sellers as selling stolen items and yes, there is a requirement for a police report. Since the mdse was not stolen from me, I coudn't persue the matter.
I don't think you're irresponsible; I totally understand how these things can sometimes grow legs and run away!
I thought I'd lost my badge and that is how I came to search ebay for a replacement. Then, about 6-9 months later, after buying other badges but not one exactly like the lost one, I put on a winter blazer and in the pocket I found my badge! I couldn't remember how it got in that pocket... I've been more careful, but I have truly lost one badge since then (though I'm 99.99% sure it was eaten by my washing machine - I've rescued another one in the machine though its guard is gone....)

