A supervisor cannot communicate to other staff that any disciplinary action took place. The most I will ever say, if a staff member asks me privately, is that they need to trust that I am addressing any situation that occurs if I am aware of the situation. However, I honor the confidentiality of all employees, so will make no comment about any specific person or situation. (This tells them that they will receive the same confidentiality if they experience difficulties.) Mostly, you are working to create an environment in which people feel problems and issues are addressed without violating the confidentiality of any employee.
The only time I might do something differently, or additionally, occurs when an employee is fired and another employee comes to me seeking to understand why so that he or she does not make the same mistakes. Then, I simply help them list what it takes to be a good employee and if they have one, review their performance development plan. I don't address the fired employee's issues at all.
