Q:

Is there an English version for “Unum castigabis, centum emendabis”?

The Latin saying Unum castigabis, centum emendabis  is commonly and currently used in Italian as “punirne uno per educarne cento”. 
Literally the expression means “punish one, to correct one hundred”. It may apply to different contexts where a leader or a boss wants to convey a strong message to a group of people. An employee, for instance might be  fired without being given a second chance just to show other employees that they may be fired too if they don’t give their utmost. It is a way to intimidate. 
Is there an English saying that conveys the same concept? 

A:

The saying has been translated into English before. One research paper from 2018 translated the saying in the title: "Punish One, Teach One Hundred: The Sobering Effect of Punishment on the Unpunished." A footnote connects the title to the Latin expression as well as a saying by Chairman Mao:

In Latin, “Unum castigabis centum emendabis.”  A similar prescription stating “Punish One, Teach a Hundred” is often attributed to Mao Tse-Tung.

More perplexing is compliance officer Kristy Grant-Hart attributing the same phrasing to the mafia in a 2017 blog post:

The Mafia has a saying: “Punish one, teach 100.”  I’m certain this works for criminal enterprise and I’m equally sure it works in corporations as well.  This saying reminds us that what happens to one person teaches many others about the consequences of their behaviour.

The idiom make an example (out) of (someone) has a similar meaning. Merriam-Webster has one version of this, "make an example of":

to punish (a person who has done something wrong) as a way of warning other people not to do the same thing

In other words, singling out one disobedient person in a group and giving them a harsh punishment makes an example of that person to their peers, the theory being that they'll be less likely to commit the same act.

