I have heard of a scam with firefighters, and it wouldn't surprise me if police do a similar thing.

There are standards for how many firemen are required to be working: https://www.iaff.org/wp-content/uploads/Departments/Fire_EMS...

To increase their take-home pay, firemen call in sick on a coordinated, rotating schedule, and the minimum staff requirements force off-duty firemen to be called in to work and get paid overtime.