I've never heard of this policy ever existing, anywhere. I doubt it does. What does happen is that companies are always trying to cut costs from the top down.

In a hypothetical well run company, everyone tries to save unnecessary costs.

In most companies, it's a constant battle of higher management trying to cut costs and those lower down the rung wanting to get the job done and go home with the minimum of stress.

Lower management want to hit budget to not get bollocked / to get their bonuses, but they don't actually give a shit about the company's bottom line. If they can spend the money on stuff that will make their employees happier and make the work go smoother without those above them getting pissy, they usually will.

Why not give bonuses for reducing costs? That's really hard to do well. Likelihood is you'll just have managers completely fuck the business long term to hit short term targets. Better for them to not cut costs all the way they can than to gut the company in a year.