If your workforce is inventing tons of reasons to get time off work, you have an issue with the work environment, the work load, the hiring process...
There are bigger issues going on.
Not one single person where I work, would fake reasons to get off work. We adore our job, we've stuck with it from start up where things were scrappy, pay was low, hours weird.
We love our work - we have a boss who listens, we are a team that trust one another, supports one another, there is no need, it does not happen!
Thats not just the case with us sub contractors either - our salaried team are the same. One of our IT team was answering questions and fixing shit on their wedding day! My immediate boss will absolutely check in and answer questions whilst on holiday. The sub contractors regularly cover each others shifts, and frequently refuse to claim the hours worked, insisting the person whose shift it is has the hours, so it isn't even about the money.
I wouldn't even have to ask for time off when a pet dies, I'd BE asked if I wanted it.