Yeah it's a sunk cost fallacy. 91 days x 13 hours = 1,183 hours. Even assuming the manager is making $10 an hour they wouldn't recoup the loss unless they found it early.

Ofc no manager makes $10/hour.

Let's make some assumptions. just picking a retail place with firearms managers and i see cabela's listed on glassdoor reporting $53-91k. Let's go with the low end 53k. Let's also assume 40 hours per week and the manager is doing no more than 20% unpaid hours, so 2080 salary hours + 208 "good worker" hours = 2288 total hours worked in a year. 53k salary / 2288 hours = $23/hour effective pay rate. That's even before considering the benefits package

$10,000 item / $23 per hour = ~435 hours of real time footage before it is a guaranteed sunk cost. This means finding it within first ~37% of footage. Meanwhile 435 hours would effectively take the manager off the floor for a quarter of the year.

I didn't need to do math to tell you that this is a task given to someone to make them quit. Manager did something else and this how the company decided to get rid of them.